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Machine Learning and Deep Learning

Exploring the Advantages of Quantum Generative Adversarial Networks in Generative Chemistry
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  • Po-Yu Kao
    Po-Yu Kao
    Insilico Medicine Taiwan Ltd., Taipei 110208, Taiwan
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    Orcidhttps://orcid.org/0000-0002-9439-8819
  • Ya-Chu Yang
    Ya-Chu Yang
    Insilico Medicine Taiwan Ltd., Taipei 110208, Taiwan
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  • Wei-Yin Chiang
    Wei-Yin Chiang
    Hon Hai (Foxconn) Research Institute, Taipei 114699, Taiwan
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  • Jen-Yueh Hsiao
    Jen-Yueh Hsiao
    Hon Hai (Foxconn) Research Institute, Taipei 114699, Taiwan
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  • Yudong Cao
    Yudong Cao
    Zapata Computing, Inc., Boston, Massachusetts 02110, United States
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  • Alex Aliper
    Alex Aliper
    Insilico Medicine AI Limited, Masdar City, Abu Dhabi 145748, UAE
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  • Feng Ren
    Feng Ren
    Insilico Medicine Shanghai Ltd., Shanghai 201203, China
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  • Alán Aspuru-Guzik
    Alán Aspuru-Guzik
    Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada
    Department of Computer Science, University of Toronto, Toronto, ON M5S 2E4, Canada
    Vector Institute for Artificial Intelligence, Toronto, ON M5S 1M1, Canada
    Lebovic Fellow, Canadian Institute for Advanced Research, Toronto, ON M5S 1M1, Canada
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    Orcidhttps://orcid.org/0000-0002-8277-4434
  • Alex Zhavoronkov*
    Alex Zhavoronkov
    Insilico Medicine Hong Kong Ltd., Hong Kong SAR, 999077, China
    *E-mail: [email protected]
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  • Min-Hsiu Hsieh*
    Min-Hsiu Hsieh
    Hon Hai (Foxconn) Research Institute, Taipei 114699, Taiwan
    *E-mail: [email protected]
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  • Yen-Chu Lin*
    Yen-Chu Lin
    Insilico Medicine Taiwan Ltd., Taipei 110208, Taiwan
    Department of Pharmacy, National Yang Ming Chiao Tung University, Taipei 112304, Taiwan
    *E-mail: [email protected]
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Open PDFSupporting Information (1)

Journal of Chemical Information and Modeling

Cite this: J. Chem. Inf. Model. 2023, 63, 11, 3307–3318
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https://doi.org/10.1021/acs.jcim.3c00562
Published May 12, 2023

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Abstract

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De novo drug design with desired biological activities is crucial for developing novel therapeutics for patients. The drug development process is time- and resource-consuming, and it has a low probability of success. Recent advances in machine learning and deep learning technology have reduced the time and cost of the discovery process and therefore, improved pharmaceutical research and development. In this paper, we explore the combination of two rapidly developing fields with lead candidate discovery in the drug development process. First, artificial intelligence has already been demonstrated to successfully accelerate conventional drug design approaches. Second, quantum computing has demonstrated promising potential in different applications, such as quantum chemistry, combinatorial optimizations, and machine learning. This article explores hybrid quantum-classical generative adversarial networks (GAN) for small molecule discovery. We substituted each element of GAN with a variational quantum circuit (VQC) and demonstrated the quantum advantages in the small drug discovery. Utilizing a VQC in the noise generator of a GAN to generate small molecules achieves better physicochemical properties and performance in the goal-directed benchmark than the classical counterpart. Moreover, we demonstrate the potential of a VQC with only tens of learnable parameters in the generator of GAN to generate small molecules. We also demonstrate the quantum advantage of a VQC in the discriminator of GAN. In this hybrid model, the number of learnable parameters is significantly less than the classical ones, and it can still generate valid molecules. The hybrid model with only tens of training parameters in the quantum discriminator outperforms the MLP-based one in terms of both generated molecule properties and the achieved KL divergence. However, the hybrid quantum-classical GANs still face challenges in generating unique and valid molecules compared to their classical counterparts.

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Introduction

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The drug development process includes discovery and development, preclinical research, clinical research, Food and Drug Administration (FDA) review, and FDA postmarket safe monitoring. The entire process is time- and resource-consuming and has a low probability of success, with ∼4% of preclinical drugs being eventually granted license. (1) The average time for a new medicine to complete the journey from initial discovery to the marketplace takes at least ten years. (2) The estimated median capitalized research and design (R&D) cost per new drug (accounting for the cost of failures) was $985 million between 2009 and 2018. (3) Recent advances in machine learning and deep learning technology have improved and reduced the cost of pharmaceutical R&D. (4−9) For example, our team (10) discovered potent inhibitors of discoidin domain receptor 1 (DDR1), a kinase target implicated in fibrosis and other diseases, in 21 days. Chan et al. (11) estimated their machine learning algorithms would shrink the drug candidate identification phase from a few months to one year.
De novo drug design refers to a novel chemical compound design with desired pharmacological and physicochemical properties. (12) The discovery of novel chemical compounds with desired biological activities is a critical step to keep the drug discovery pipeline moving forward. (13) It is also crucial for developing novel therapeutics for patients. (14) Conventional approaches include ligand-based drug design (LBDD), fragment-based drug design (FBDD), and structure-based drug design (SBDD). LBDD is based on known active binders of a biological target, and FBDD identifies small molecular fragments with weak affinity for a biomolecular target of interest and assembles them into fully druglike compounds. (15) Aside from LBDD and FBDD, SBDD is based on the properties of the active site of a biological target.
Artificial intelligence (AI) has made a breakthrough in the recent de novo molecule design. (16−18) We identify four well-known generative machine learning algorithms (19) in the field: evolutionary algorithms (EA), recurrent neural networks (RNNs) (such as gated recurrent unit (GRU) and long short-term memory (LSTM)), autoencoders (such as adversarial autoencoder (AAE) and variational autoencoder (VAE)), (20) and generative adversarial network (GAN). GAN (21) has become a popular network architecture for generating highly realistic data, (22) and it has shown remarkable results for generating data that mimics a data distribution in different tasks. (23−26) GAN consists of a generator and a discriminator defined by an artificial neural network (ANN). The parameters of a GAN can be learned by back propagation. The generator takes random noises as input and tries to imitate the data distribution, and the discriminator tries to distinguish between the fake and real samples. A GAN is trained until the discriminator cannot distinguish the generated data from the real data.
GANs are one of the most successful generative models in the drug discovery field, and several different GAN architectures have been proposed in the past decades in de novo drug discovery. (27−29) Zhavoronkov et al. (10) proposed a deep generative model called generative tensorial reinforcement learning (GENTRL) for de novo small-molecule generation. The GENTRL generates novel drugs with better synthetic feasibility and biological activity. Guimaraes et al. (30) proposed an objective-reinforced generative adversarial network (ORGAN) that combines the GAN and reinforcement learning (RL) algorithm. ORGAN is built on SeqGAN (31) and is the first GAN architecture in the de novo molecule generation. It is a sequential generative model operating on simplified molecular-input line-entry system (SMILES) string representations of molecules. The generated samples of ORGAN maintain information originally learned from data, retain sample diversity, and show improvement in the desired drug properties. Prykhodko et al. (32) presented a novel neural network architecture called LatentGAN for de novo molecular design. It combines an autoencoder and a generative adversarial neural network. The generator and discriminator of LatentGAN take n-dimensional vectors as inputs. These inputs derived from the code layer of an autoencoder are trained as a SMILES heteroencoder. (33) This method allows LatentGAN to focus on optimizing the sampling without worrying about SMILES syntax issues. Cao and Kipf introduced MolGAN (34) for small-molecule de novo design, which operates directly on graph-structured data. It is the first GAN to address the generation of graph-structured data in the context of molecular generation. MolGAN is demonstrated to generate close to 100% valid compounds in experiments on the quantum machines 9 (QM9) chemical database. The generated molecules of MolGAN have better chemical properties particularly in synthesizability and solubility than the generated compounds of ORGAN. Neither ORGAN nor MolGAN is directly compared with LatentGAN in the paper. These generative models have the potential to be improved with quantum machine learning algorithms.
The applications of quantum computing can be found in different fields, such as solving routing problems, (35,36) stock price forecasting, (37,38) multitask classification, (39) the two-player zero-sum game, (40) high-resolution handwritten digits generation, (41) the discovery of molecular properties, (42−49) tautomeric state prediction, (50) and drug design. (51,52) We can obtain more efficient and accurate results by utilizing the technique of quantum annealer, quantum machine learning, and quantum algorithm. These advantages that utilize the fundamental properties of quantum mechanics to achieve better performances, compared to the classical methods, are called quantum advantages. Several studies have demonstrated that variational quantum circuit (VQC) (53) performs the advantages in expression power, (54) learnability, (55) and robustness. (56) It indicates that VQC can greatly boost the solution to the problem, e.g., drug discovery, which is hard to tackle by the classical neural network.
Quantum generative adversarial network (QuGAN) (57) provided the first theoretical framework of quantum adversarial learning. QuGAN’s exponential advantages over classical GANs directly result from the ability of quantum information processors to represent N-dimensional features using log N qubits with time complexity of O(poly(log N)). Recent studies also showed that generative models implemented by quantum circuits with fewer architectural complexities could easily bypass their classical counterparts. (52,58) Dallaire-Demers et al. provided the first feasible implementation of QuGAN using quantum circuits in a simulator. (59) Analogous proposals of QuGAN for continuous functions have been proposed during the same period. (60) Later on, QuGANs demonstrated its first successful training on the MNIST dataset on a physical quantum device. (58) Li et al. (52) pushed the research to the real world further by showing the QuGANs can learn or generate the distribution of the QM9 dataset, which provides the quantum chemical properties for small organic molecules in drug design. However, the source code (61) they provided struggles with generating training-set-like molecules. In addition, it lacks a detailed comparison between the generated samples from QuGAN and those from classical GAN.
In this work, we perform the training tasks on the QM9 dataset using the classical and quantum GAN. We not only demonstrate that the quantum GAN outperforms the classical GAN in the drug properties of generated compounds and the goal-directed benchmark but ensure that the trained quantum GANs can generate training-set-like molecules by using the variational quantum circuit as the noise generator. In addition, we show the potential of the variational quantum circuit in the generator of GAN to generate small molecules. In the end, we demonstrate that the quantum discriminator of GAN outperforms the classical counterpart in terms of generated molecule properties and KL-divergence score.

Computational Results and Discussion

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In this study, we would like to computationally explore the potential benefits of our algorithms as compared to classical algorithms in small molecule discovery. We endeavored to find the best hyper-parameters for the base MolGAN. We first examined different complexities of generators and observed that MolGAN-HR (high reduction) has the best performance, compared to other generator complexities (see Table S1 in the Supporting Information). We then examined different input noise dimensions of generators and determined that the number of unique and valid molecules saturated at the input dimension was equal to 4 (z_dim = 4) (see Table S2 in the Supporting Information). In addition, we also tested different numbers of parametrized layers in the variational quantum circuit (VQC) and observed that MolGAN-HR with three parametrized layers of VQC as a noise generator has the best performance, compared to other numbers of parametrized layers (Table S3 in the Supporting Information). Therefore, in the following experiments, MolGAN-HR is used as the base model, and VQC with three parametrized layers is used as the base quantum circuit.
In the first experiment, we substitute the noise generator of MolGAN with a VQC and discover the quantum advantage in the generated molecules with better drug properties. In the second experiment, we replace the generator of MolGAN with a VQC and show the potential of generating small molecules using a VQC. In the third experiment, we supplant the discriminator of MolGAN with a VQC and demonstrate the quantum advantage. Figure 1a illustrates different combinations of the classical/quantum noise/generator/discriminator, and their corresponding model name is shown in Table S4 in the Supporting Information. MolGAN uses a classical noise generator, a generator, and a graph-based discriminator. QuMolGAN uses a quantum noise generator, a classical generator, and a classical graph-based discriminator. MolGAN-QC uses a classical noise generator, a quantum generator, and a classical graph-based discriminator. MolGAN-CQ uses a classical noise generator, a classical generator, and a quantum discriminator. MolGAN-CC uses a classical noise generator, a classical generator, and a classical MLP-based discriminator. All experiments are implemented by using Pennylane (63) and PyTorch. (64)

Figure 1

Figure 1. Overall pipeline. (a) The overall pipeline of MolGAN with different combinations of classical/quantum components. The reward neural network branch is enabled in the goal-directed benchmark. The classical noise generator samples from the Gaussian distribution, and the quantum one uses the variational quantum circuit (VQC). The classical generator is built by neural networks, and the quantum one uses the patch-based VQC to generate the molecular graph. The molecular graph is represented by a bond matrix and atom vector. The classical discriminator is built by a graph-based neural network or multilayer perceptron (MLP), and the VQC is used in the quantum one. (b) The example of VQC in the noise generator. (c) The patch method uses multiple VQCs as subgenerators. Each subgenerator takes noise as input and outputs a partial part of the final molecular graph. The final molecular graph is constructed by concatenating all the partial patches together. (d) The example of VQC in the quantum generator. (e) The VQC of the quantum discriminator consists of the amplitude embedding circuit (Sx), the strong entanglement layers (Uθ), and the measurement. (f) The VQC of strongly entanglement layers contains multiple CNOT gates and parametrized rotational gates (R). (g) MLP-based discriminator architecture in MolGAN-CC.

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Quantum Noise Generator

In the first experiment, we would like to compare the performance of QuMolGAN and classical MolGAN. We have examined different qubits for VQC and found that its performance saturates at 4 qubits (Table S5 in the Supporting Information). In addition, we have also tested different numbers of parametrized layers in the VQC and observed that QuMolGAN with three parametrized layers of VQC as a noise generator has the best performance, compared to other numbers of parametrized layers (Table S3). We use the same hyperparameters to train the QuMolGAN and MolGAN, (34) except for the learning rate. The learning rate of the quantum noise generator is 0.04, and the learning rate for the generator and discriminator is 0.001. The models are trained for 150 epochs. The WGAN (Wasserstein generative adversarial networks) loss (65) is used to train the models. QuMolGAN with three parametrized layers is used in this experiment. We have examined the input dimension of the generator at 2, 3, and 4, and the results are shown in Table 1. The performance of MolGAN and QuMolGAN saturates at z_dim = 4. It is noted that the QED, Solute, and SA scores in this table are calculated from the valid and unique molecules. The QuMolGAN is lacking in generating as many molecules as classical MolGAN which results in worse KL Scores. However, the QuMolGAN can generate molecules with significantly (p < 0.05) better drug properties, compared to the MolGAN, particularly when the input noise dimension is small (z_dim = 2 and z_dim = 3). The drug properties distributions of MolGAN-generated and QuMolGAN-generated molecules are shown in Figure 2a for z_dim = 2. It shows that QuMolGAN can generate molecules with better drug properties, particularly in QED. QuMolGAN has less probability to generate molecules whose QED is <0.4. For the KL-divergence task, the MolLogP, BertzCT, and MolWt distributions of generated molecules are also shown in Figure 2b for z_dim = 2. The classical MolGAN (black) tends to generate molecules with similar distributions to the training set (gray), which results in a better KL-divergence score. In the end, we randomly sample 12 valid and unique molecules from both MolGAN and QuMolGAN for z_dim = 2, and the example molecules are shown in Figures 3a and 3b, respectively. QuMolGAN can generate training-set-like molecules with better drug properties.
Table 1. Comparing Generated Molecules of QuMolGAN and MolGAN in Drug Propertiesa
 z_dim = 2z_dim = 3z_dim = 4
 QuMolGANMolGANp-valueQuMolGANMolGANp-valueQuMolGANMolGANp-value
number of moleculesb363657–4142163–5113085–
QED ↑0.4890.475<0.010.4890.465<0.010.4730.465<0.05
solubility ↑0.3430.324<0.050.3700.305<0.010.3170.298<0.01
SA ↑0.3670.336<0.050.3100.307<0.050.3080.2960.246
KL score (S)c ↑0.6530.824–0.7970.913–0.8460.957–
a

Bold numbers highlight the better scores in QuMolGAN, compared to the corresponding MolGAN. Note that the QED, Solute, and SA scores in this table are calculated from the valid and unique molecules.

b

Number of valid and unique molecules from 5000 samples.

c

From eq 2.

Figure 2

Figure 2. Property distributions of molecules. (a) Drug properties distributions (left to right: QED, SA, and Solute) from valid and unique MolGAN-generated (in blue) and QuMolGAN-generated (in orange) molecules. (b) KL-divergence distributions (left to right: MolLogP, BertzCT, and MolWt) of valid and unique MolGAN-generated (blue), QuMolGAN-generated (orange), and QM9 (gray) molecules. (c) KL-divergence distributions (from left to right: MolLogP, BertzCT, and MolWt) of MolGAN-CC-ER-generated (orange), MolGAN-CQ-generated (yellow), MolGAN-generated (blue), and QM9 (gray) molecules.

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Figure 3

Figure 3. Example molecules. (a) Example molecules of MolGAN with z_dim = 2. (b) Example molecules of QuMolGAN with z_dim = 2. (c) Example molecules of MolGAN-CQ.

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Goal-Directed Benchmark

As mentioned in ref (66), the goal-directed optimization of molecules tries to improve the demanded scores for the generated molecules. These scores reflect how well molecules satisfy the required properties. The goal is to find molecules that maximize the scoring function. In this experiment, we also would like to check if the quantum circuit can bring advantages to the MolGAN in the goal-directed benchmark. Therefore, we enable the reward network branch of the original schema as shown in the gray block in Figure 1a. At this time, the generator is trained using a linear combination of the WGAN (65) loss and the RL (67) (reinforcement learning) loss:
L(ω)=αLWGAN(ω)+(1−α)LRL(ω)
(1)
where α ∈ [0, 1] is a hyperparameter that controls the tradeoff between WGAN loss and RL loss, and ω are the inputs to networks. Here, we set α = {1.0, 0.5, 0.01} to weigh the loss between two components and the goal of improving SA, and QED to train MolGAN and QuMolGAN, as suggested by the medical chemists. In addition, we also add the unique score into the goal to prevent the model from generating the same molecules. We have trained MolGAN and QuMolGAN with (α = {0.5, 0.01}) and without (α = 1.0) RL loss using the same hyperparameters for 150 epochs, and the results are shown in Table 2. The input noise dimension to the generator is 4 (z_dim = 4). It is noted that the QED, Solute, and SA scores in this table are calculated from the valid molecules. In this table, the KL Scores of MolGAN are always greater than their quantum counterparts in different weights of RL loss. However, QuMolGAN can achieve a higher goal (from 0.47 to 0.57 in QED and from 0.29 to 0.76 in SA), compared to MolGAN (from 0.47 to 0.52 in QED and from 0.30 to 0.60 in SA) while α = 0.01. The solute is not the goal so these scores are close for MolGAN and QuMolGAN.
Table 2. Performance Comparison between MolGAN and QuMolGAN with (α = {0.5, 0.01}) and without (α = 1.0) Reinforcement Learning Loss in the Goal-Directed Benchmarka
 MolGANQuMolGAN
 α = 1.0α = 0.5α = 0.01α = 1.0α = 0.5α = 0.01
number of moleculesb28902700696534309116
validity ↑80.4078.4868.7670.0270.3242.94
uniqueness ↑71.8968.8120.2415.258.785.40
QED ↑0.470.480.520.470.490.57
Solute ↑0.310.310.450.320.300.44
SA ↑0.300.310.650.290.280.76
KL Score (S)c ↑0.950.940.580.920.820.31
a

Note that the QED, Solute, and SA scores in this table are calculated from the valid molecules. Bold numbers indicate better scores among the same type of models with different RL weights α, and the underlined numbers indicate the best scores across different types of models.

b

Number of valid and unique molecules from 5000 samples.

c

From eq 2.

Quantum Generator

In the second experiment, we try to benchmark the advantage of the quantum circuit in the generator of GAN. We have tried to substitute the generator of MolGAN with a VQC described in ref (58) for the small molecule generation. The performance of MolGAN with the quantum generator (MolGAN-QC) is reported in Table 3.
Table 3. Performance of MolGAN with the Quantum Generatora
# epochnumber of moleculesbvalidity ↑uniqueness ↑novelty ↑diversity ↑QED ↑solubility ↑SA ↑KL Score (S)c ↑
17379.394.491001.000.430.750.240.24
25476.373.451001.000.470.750.240.25
34378.472.681001.000.480.750.110.28
42978.611.801001.000.480.750.130.29
53077.931.881001.000.480.750.140.30
64078.372.491001.000.480.750.090.21
72980.271.761001.000.470.750.060.28
83978.912.411001.000.480.750.160.28
94174.662.681001.000.480.750.220.25
102979.741.781001.000.480.750.080.27
a

The QED, Solute, and SA scores in this table are calculated from the valid molecules.

b

Number of valid and unique molecules from 2048 samples from Gaussian distribution.

c

From eq 2.

Although the integration works smoothly, the training processing is time-consuming and resource-consuming. The average training time per step takes ∼39 s in the Amazon EC2 C6a Metal Instance, which results in ∼3.5 days per epoch. In addition, the model has difficulty generating more valid and unique molecules after being trained for ten epochs. It fails to generate the training-data-like molecules, even after 10 epochs of training. Random-picked and cherry-picked examples of generated molecules are shown in Figure S1. Most generated molecules are similar to the randomly sampled molecules in Figure S1. However, we demonstrate that the quantum generator has the potential to generate small molecules.

Quantum Discriminator

In the third experiment, in addition to substituting the generator architecture, the architecture with a quantum discriminator combined with the classical generator described in MolGAN has been examined. Our goal is to determine if the quantum discriminator shows any advantage over its classical counterparts. We have found that the number of learnable parameters is significantly less than the classical ones, while the model can still generate valid molecules. Furthermore, to conduct a fair comparison between the classical discriminator and the quantum one, we changed the MolGAN classical graph-based discriminator to the multiple-layer perceptron (MLP) architecture, which is more similar to our proposed quantum discriminator architecture, reduced the number of its training parameters, and found that quantum discriminator with 50 training parameters outperforms the classical discriminator with 22,500 parameters in terms of generated molecule properties and KL divergence. For simplicity, all the combinations of the classical/quantum noise/generator/discriminator are listed in Table S4. In this experiment, the noises of the generator are always sampled from the Gaussian distribution.
In the following subparagraphs, we first present our proposed MolGAN-CQ and the training details. Second, we compare the results of MolGAN-CQ with MolGAN. In the end, we made architecture modifications from the Graph-Classical-Discriminator in MolGAN to the MLP-Classical-Discriminator (MolGAN-CC) and reduced the amount of the learnable parameters to make a fair comparison with MolGAN-CQ.

MolGAN-CQ Architecture and Training Details

As illustrated in Figure 1a, the MolGAN-CQ consists of three components: a classical noise generator, a classical generator, and a quantum discriminator. To encode two generator outputs, a bond matrix and an atom vector, into the quantum discriminator efficiently, we first flatten the bond matrix into a vector, which is subsequently concatenated with the atom vector to a new vector with a size of 450. After that, the resulting vector will be the input of the Q-Discriminator, composed of an amplitude embedding layer followed by three strongly entangling layers as described in Figure 1e. For the training details, at first, we followed the best hyperparameters set in MolGAN. However, applying the same training details on MolGAN-CQ makes the training process hard to converge. Therefore, we change the learning rate from 1 × 10–3 to 1 × 10–4 for the generator to make it more stable. Moreover, we have experimented with the alternating training times between the classical generator and quantum discriminator with several sets, including (G, D)=(1, 5), (1, 8), (1, 10). We found out that training 1 step C-Generator followed by 10 steps Q-Discriminator stabilizes the training process. The other hyperparameters remain identical to the ones in MolGAN.

Comparison with Classical MolGAN

In this section, we compare MolGAN-CQ with MolGAN. We trained MolGAN according to the best hyperparameter sets found in the previous section. Notice here, since training a quantum network is time-consuming, and the loss curve from classical MolGAN at epoch 30 shows the trend of convergence, both MolGAN-CQ and MolGAN were only trained to epoch 30 and evaluated at epoch 30 instead of epoch 150. After that, both models generate 5000 samples to do a further comparison. Table 4 demonstrates that MolGAN-CQ can generate valid and druglike molecules. In addition, MolGAN-CQ can generate molecules with better drug properties, particularly in Solute and SA. However, compared to classical MolGAN, MolGAN-CQ does not have an advantage in KL divergence with training data probability. Figure 3c shows some molecules generated from MolGAN-CQ.
Table 4. Performance Comparison between MolGAN and MolGAN-CQa
 MolGANMolGAN-CQ
# of moleculesb2693730
Validity ↑7631.34
Uniqueness ↑70.8746.59
QED ↑0.470.48
Solute ↑0.310.44
SA ↑0.310.66
KL Score (S)c↑0.940.75
a

The models are only trained for 30 epochs. Bold numbers indicate better scores. The QED, Solute, and SA scores in this table are calculated from the valid molecules.

b

Number of valid and unique molecules from 5000 samples.

c

From eq 2

Comparison with MolGAN-CC

In this section, MolGAN-CQ is compared with MolGAN-CC with different numbers of hidden layers to evaluate MolGAN-CQ’s capacity. To have a fair comparison, we modified the original graph-based network to a multiple-layer perceptron (MLP), as shown in Figure 1g. Under this condition, the input of the MLP-based discriminator would be the same as the one in MolGAN-CQ’s quantum discriminator, a flattened vector instead of a graph. The network architecture of MolGAN-CC consists of a classical noise generator, a classical generator, and the classical MLP-based discriminator, as shown in Figure 1a. Furthermore, since the discriminator of MolGAN-CQ only has 50 learnable parameters, we have tried to reduce the discriminator size of MolGAN-CC as small as possible for a fair and reasonable evaluation. However, the input vector is already a size of 450, it is not possible to decrease the parameter size to 50 in the classical MLP. Therefore, we have tried MolGAN-CC with three different parameter sizes of discriminator, as shown in Table S6 in the Supporting Information. MolGAN-CC-ER (extremely reduction) has three layers with sizes (450, 50, 1) in the discriminator, and the total parameter size is 22 000. MolGAN-CC-HR (highly reduction) has three layers with size (450, 100, 1) in the discriminator, and the total parameter size is 45 000, MolGAN-CC-NR (no reduction) has four layers with sizes (450, 150, 50, 1) in the discriminator, and the total parameter size is 82 000.
Table 5 demonstrates that, although MolGAN-CC-NR and MolGAN-CC-HR have a higher capacity to generate molecules whose molecule properties are more similar to the training data, MolGAN-CQ with only 50 parameters can achieve an outstanding performance, compared to MolGAN-CC-ER with 22K parameters in terms of KL-score which shows the quantum advantage in the expression power. The distributions of molecular properties of MolLogP, MolWt, and BertzCT, generated from MolGAN-CC-ER, MolGAN-CQ, MolGAN, and QM9, are shown in Figure 2c. As we can see from Figure 2c, molecular properties from MolGAN are closer to the ones from the training data, QM9, compared to MolGAN-CQ and MolGAN-CC-ER. Nevertheless, MolGAN-CQ with only 50 parameters could generate molecules with similar distribution to the training data in comparison to MolGAN-CC-ER with 22 000 parameters.
Table 5. Performance Comparison between MolGAN-CQ and MolGAN-CC with Three Different Sizes of the MLP-Based Discriminatora
 MolGAN-CQMolGAN-CC-ERMolGAN-CC-HRMolGAN-CC-NR
number of parameters5022K45K82K
number of moleculesb73010419192284
Validity ↑31.3499.7844.154.7
Uniqueness ↑46.592.0887.0383.51
QED ↑0.480.510.490.5
Solute ↑0.440.630.350.38
SA ↑0.660.970.480.50
KL Score (S)c↑0.750.280.840.81
a

Bold numbers indicate better performance across different types of models. The QED, Solute, and SA scores in this table are calculated from the valid molecules.

b

Number of valid and unique molecules from 5000 samples.

c

From eq 2

Conclusions

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In this paper, we have explored the quantum advantage in small-molecule drug discovery by substituting each part of MolGAN (34) with a VQC step by step and comparing its performance with the classical counterpart. In the first experiment, using a VQC as a noise generator to the classical GAN can generate small molecules with better drug properties, including QED, SA, and LogP, particularly when the input dimension to the generator is small, e.g., z_dim = 2 or z_dim = 3. However, QuMolGAN has difficulty generating as many unique molecules compared to classical MolGAN, which results in a lower KL Score. In addition, this hybrid model achieves better performance in the goal-directed benchmark, compared to the classical counterpart. In the second experiment, we substitute the classical generator with a VQC with the patch method. (58) We demonstrated the potential of generating training-set-like small molecules using a quantum generator. However, the training processing is resource-consuming and time-consuming, even in the advanced classical computer. In the third experiment, we replace the classical discriminator with a VQC and compare its performance with the classical counterpart. This hybrid model MolGAN-CQ outperforms the classical counterpart, in terms of generated molecule properties and the KL score. We also demonstrated that the hybrid model could generate valid molecules with only tens of learnable parameters in a quantum discriminator. The proposed hybrid model has the potential to be integrated into the Insilico Medicine Chemistry42 (62) platform (see Figure S2 in the Supporting Information).
Finally, expressive power illustrates the capability of a model to capture the distribution of the target features. Increasing model complexity can normally enhance this capability. In our work, we demonstrate that a quantum circuit consisting of only 50 learnable parameters is able to generate a distribution similar to what classical generates but with 20K learnable parameters. Therefore, the quantum advantage in expressive power is observed.

Materials and Methods

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In this section, we will first introduce the evaluation method and metrics followed by the dataset, we used to train the generative models. Then, the methodologies will be introduced.

Evaluation Method and Metrics

To evaluate the performance of different generative models, we first generate 5000 noise samples from Gaussian distribution and variational quantum circuits for MolGAN and QuMolGAN, respectively. The generated noise samples are then fed into the trained generator of models to produce the atom vectors and bond matrices. In the end, these vectors and matrices are used to construct the molecular graphs. Seven evaluation metrics described below will be calculated from the molecular graphs.
Three quality metrics, i.e., validity, uniqueness, and novelty used in refs (68) and (69) and three drug properties, i.e., quantitative estimation of drug-likeness (QED), solubility, and synthesizability (SA), is used to compare different generative models in this work. Validity is the ratio of the valid molecules to all generated molecules, and uniqueness is the ratio of unique molecules to the valid molecules. Novelty is defined as the ratio of valid molecules that are not in the training dataset to all valid molecules. In addition, we also measure the diversity of generated molecules which is defined as how likely the generated molecules are to be diverse to the training dataset. We also report the valid and unique molecules (number of molecules) from 5000 noise samples. QED (70) measures how likely a molecule is to be a drug based on the concept of desirability. Solubility reports the n-octanol–water partition coefficient (logP) (71) of the molecule that is the degree of a molecule being hydrophilic. SA (72) quantifies how easy a molecule is to be synthesized based on the molecular complexity and fragment contributions. These property metrics are calculated by using RDKit. (73)
The Kullback–Leibler (KL) divergences (74) are also calculated, and it measures how well a probability distribution approximates another distribution. The probability distributions of a variety of physicochemical descriptors including BertzCT (molecular complexity index), MolLogP (Wildman-Crippen LogP value (71)), MolWt (molecular weight), TPSA (molecular polar surface area), NumHAcceptors (number of hydrogen acceptors), NumHDonors (number of hydrogen donors), NumRotatableBonds (number of rotatable bonds), NumAliphaticRings (number of aliphatic rings), and NumAromaticRings (number of aromatic rings) for the generated molecules and the molecules of the training set are compared, and the corresponding KL-divergence scores DKL,i are computed. Models able to capture the distributions of molecules in the training set will lead to small KL-divergence scores (DKL). However, the final KL-divergence score (S) (66) used in this paper is computed by
S=19∑i=19exp(−DKL,i)
(2)
Therefore, the larger final KL-divergence score (S) represents how well the model can capture these nine physicochemical distributions of molecules in the training set.

Dataset

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All experiments of this work use the QM9 (Quantum Machines 9) (75) dataset. The QM9 dataset is curated from the GDB-17 chemical database, (76) which has ∼166.4 billion molecules. QM9 consists of 133 171 molecules containing less than or equal to nine non-hydrogen atoms (carbon, nitrogen, oxygen, and fluorine). Figure S3 in the Supporting Information shows some molecules from the QM9 dataset, and the average QED, solubility, and SA of those 133 171 molecules are 0.461, 0.289, and 0.327, respectively.

Methodology

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Variational Quantum Circuits (VQCs)

A Quantum gate is a basic quantum circuit operating on a small number of qubits. In this work, two controlled gates (Controlled-X gate and Controlled-Z gate) and four single-qubit rotations (Rx, Ry, Rz, and R) are used to construct the variational quantum circuit. Controlled-X (CNOT) gate is a two-qubit operation, where the first qubit is usually referred to as the control qubit and the second qubit as the target qubit.
CNOT=[1000010000010010]
(3)
A Controlled-Z (CZ) gate is a two-qubit operation defined as
CZ=[100001000010000−1]
(4)
The Rx, Ry, and Rz gates are the essential rotation operators in the quantum circuit. The Rx gate is a single-qubit rotation through an angle θ in radians around the x-axis, and it is defined as
Rx(θ)=(cos(θ/2)−isin(θ/2)−isin(θ/2)cos(θ/2))
(5)
The Ry gate is a single-qubit rotation through an angle θ in radians around the y-axis, and it is defined as
Ry(θ)=(cos(θ/2)−sin(θ/2)sin(θ/2)cos(θ/2))
(6)
The Rz gate is a single-qubit rotation through an angle θ in radians around the z-axis, and it is defined as
Rz(θ)=(e−iθ/200eiθ/2)
(7)
The R gate is a single-qubit rotation through arbitrary angles α, β, and γ (in radians), and it can be decomposed into Ry and Rz gates. It is defined as
R(α,β,γ)=Rz(γ)Ry(β)Rz(α)=(e−i(α+γ)/2cos(β/2)−e−i(α−γ)/2sin(β/2)e−i(α−γ)/2sin(β/2)ei(α+γ)/2cos(β/2))
(8)
A variational quantum circuit (VQC) shown in Figures 1b and 1d consists of three ingredients: (1) the preparation of a fixed initial state, (2) a quantum circuit, and (3) the measurement. The initialization layer may contain Rx, Ry, Rz, and R gates, and the rotation angles are sampled from a uniform distribution or Gaussian distribution. The parametrized layers, which could be repeated for L times could have CNOT gates, CZ gates, and parametrized rotational gates whose parameters (rotation angle) can be learned through the back-propagation. The measurement takes the expected value of each qubit.

VQC of Noise Generator

In this work, MolGAN (34) is used as the base model for small molecule generation. We extend its noise generation part to the quantum domain and demonstrate the quantum advantage in the small molecule generation. MolGAN (34) is an implicit and likelihood-free generative model for small molecular graph generation. In contrast to the sequence-based models, MolGAN directly works on the graph representation of molecules. MolGAN also bypasses the requirement of expensive graph-matching procedures and node-ordering heuristics of likelihood-based methods. In the classical GANs, (21) the inputs to the generator are sampled from a distribution, e.g., uniform distribution or Gaussian distribution. Here, we would like to demonstrate the quantum advantage in the small molecule generation by utilizing a variational quantum circuit to generate the inputs of the generator, and we call this hybrid model QuMolGAN. The schema of MolGAN and QuMolGAN is shown in Figure 1a. The generator takes the noise as input and generates the molecular graph including the atom vector and bond matrix. The noise is sampled from the Gaussian distribution for the MolGAN, and the noise is generated from the VQC in Figure 1b for the QuMolGAN. The discriminator tries to distinguish between the fake molecular graph from the generator and the real molecular graph from the data distribution. More details of MolGAN can be found in the original MolGAN (34) paper.

VQC of Quantum Generator

We implement the patch method (58) in the quantum generator of MolGAN (MolGAN-QC). This method uses multiple VQCs as subgenerators, and each subgenerator is responsible for constructing a partial part of the final output, e.g., the molecular graph in this study. The final molecular graph, which consists of the atom vector and bond matrix, is constructed by concatenating all the partial patches together, as shown in Figure 1c. The subgenerator shares the same ansatz architecture as shown in Figure 1d. Each ansatz circuit consists of the preparation of the initialization state, a single layer of a 4-qubit circuit, and the measurement. The initialization layer contains Ry gates, and the rotation angles (zi) are sampled from a uniform distribution. The parametrized layers (could be repeated for L times) have CZ gates and one type of parametrized rotational gates, Ry whose parameters (θk) can be learned through back-propagation.

VQC of Quantum Discriminator

The quantum discriminator takes the molecular graph as input and determines if this molecular graph is fake (from the generator) or real (from the data distribution). The VQC of the quantum discriminator consists of the amplitude encoding layer (77) (Sx), the strongly entangling layers (Uθ) inspired by ref (78) and the measurement, as shown in Figure 1e. Amplitude encoding is used to encode the atom vector and bond matrix. The strongly entangling layers (78) have multiple CNOT gates and parametrized rotational gates R(α,β,γ), as shown in Figure 1f. In each layer, each qubit starts with parametrized rotational gates R(αi,βi,γi) followed by a CNOT gate. The parametrized angles αi,βi,γi can be learned through back-propagation. The measurement takes the expected value of one qubit, and this value is used to determine if the input molecular graph is real or fake. In our experiment, we use nine qubits to encode the molecular graph and three layers of strongly entanglement layers.

Data Availability

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The data acquisition code and source codes associated with this study are publicly available at https://github.com/pykao/QuantumMolGAN-PyTorch. The discriminator branch contains a classical/quantum noise generator, a classical generator, and a classical/quantum discriminator. This branch can be used for the quantum noise generator and the quantum discriminator. The generator branch contains a classical/quantum noise generator, a classical/quantum generator, and a classical discriminator. This branch can be used for the quantum generator.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.3c00562.

  • Different complexities of generators in MolGAN; different input noise dimensions of the generator in MolGAN-HR; different parametrized layers of QuMolGAN-HR; all the combinations of the classical/quantum noise/generator/discriminator and their corresponding model name; different numbers of qubits in the quantum circuit of QuMolGAN-HR; the details of MolGAN-CC models with the varied size of discriminators; example molecules from the quantum generator; integration of proposed hybrid generative models with Insilico Medicine Chemistry42 (62) platform; example molecules of QM9 (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Authors
    • Alex Zhavoronkov - Insilico Medicine Hong Kong Ltd., Hong Kong SAR, 999077, China;  Email: [email protected]
    • Min-Hsiu Hsieh - Hon Hai (Foxconn) Research Institute, Taipei 114699, Taiwan;  Email: [email protected]
    • Yen-Chu Lin - Insilico Medicine Taiwan Ltd., Taipei 110208, Taiwan;  Department of Pharmacy, National Yang Ming Chiao Tung University, Taipei 112304, Taiwan;  Email: [email protected]
  • Authors
    • Po-Yu Kao - Insilico Medicine Taiwan Ltd., Taipei 110208, Taiwan;  Orcidhttps://orcid.org/0000-0002-9439-8819
    • Ya-Chu Yang - Insilico Medicine Taiwan Ltd., Taipei 110208, Taiwan
    • Wei-Yin Chiang - Hon Hai (Foxconn) Research Institute, Taipei 114699, Taiwan
    • Jen-Yueh Hsiao - Hon Hai (Foxconn) Research Institute, Taipei 114699, Taiwan
    • Yudong Cao - Zapata Computing, Inc., Boston, Massachusetts 02110, United States
    • Alex Aliper - Insilico Medicine AI Limited, Masdar City, Abu Dhabi 145748, UAE
    • Feng Ren - Insilico Medicine Shanghai Ltd., Shanghai 201203, China
    • Alán Aspuru-Guzik - Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada;  Department of Computer Science, University of Toronto, Toronto, ON M5S 2E4, Canada;  Vector Institute for Artificial Intelligence, Toronto, ON M5S 1M1, Canada;  Lebovic Fellow, Canadian Institute for Advanced Research, Toronto, ON M5S 1M1, Canada;  Orcidhttps://orcid.org/0000-0002-8277-4434
  • Notes
    The authors declare no competing financial interest.

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    Approaching Target Selectivity by De Novo Drug Design
    Fischer, Thomas; Gazzola, Silvia; Riedl, Rainer
    Expert Opinion on Drug Discovery (2019), 14 (8), 791-803CODEN: EODDBX; ISSN:1746-0441. (Taylor & Francis Ltd.)
    A review. The development of drug candidates with a defined selectivity profile and a unique mol. structure is of fundamental interest for drug discovery. In contrast to the costly screening of large substance libraries, the targeted de novo design of a drug by using structural information of either the biol. target and/or structure-activity relationship data of active modulators offers an efficient and intellectually appealing alternative.: This review provides an overview on the different techniques of de novo drug design (ligand-based drug design, structure-based drug design, and fragment-based drug design) and highlights successful examples of this targeted approach toward selective modulators of therapeutically relevant targets.: De novo drug design has established itself as a very efficient method for the development of potent and selective modulators for a variety of different biol. target classes. The ever-growing wealth of structural data on therapeutic targets will certainly further enhance the importance of de novo design for the drug discovery process in the future. However, a consistent use of the terminol. of de novo drug design in the scientific literature should be sought.
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    Mouchlis, V. D.; Afantitis, A.; Serra, A.; Fratello, M.; Papadiamantis, A. G.; Aidinis, V.; Lynch, I.; Greco, D.; Melagraki, G. Advances in de novo drug design: from conventional to machine learning methods. Int. J. Mol. Sci. 2021, 22, 1676,  DOI: 10.3390/ijms22041676
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    Recent advances in fragment-based computational drug design: tackling simultaneous targets/biological effects
    Speck-Planche, Alejandro
    Future Medicinal Chemistry (2018), 10 (17), 2021-2024CODEN: FMCUA7; ISSN:1756-8919. (Future Science Ltd.)
    There is no expanded citation for this reference.
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    Mamoshina, P.; Ojomoko, L.; Yanovich, Y.; Ostrovski, A.; Botezatu, A.; Prikhodko, P.; Izumchenko, E.; Aliper, A.; Romantsov, K.; Zhebrak, A.; Ogu, I. O.; Zhavoronkov, A. Converging blockchain and next-generation artificial intelligence technologies to decentralize and accelerate biomedical research and healthcare. Oncotarget 2018, 9, 5665,  DOI: 10.18632/oncotarget.22345
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    Converging blockchain and next-generation artificial intelligence technologies to decentralize and accelerate biomedical research and healthcare
    Mamoshina Polina; Ojomoko Lucy; Aliper Alexander; Romantsov Konstantin; Zhebrak Alexander; Zhavoronkov Alex; Mamoshina Polina; Yanovich Yury; Ostrovski Alex; Botezatu Alex; Prikhodko Pavel; Izumchenko Eugene; Ogu Iraneus Obioma; Zhavoronkov Alex
    Oncotarget (2018), 9 (5), 5665-5690 ISSN:.
    The increased availability of data and recent advancements in artificial intelligence present the unprecedented opportunities in healthcare and major challenges for the patients, developers, providers and regulators. The novel deep learning and transfer learning techniques are turning any data about the person into medical data transforming simple facial pictures and videos into powerful sources of data for predictive analytics. Presently, the patients do not have control over the access privileges to their medical records and remain unaware of the true value of the data they have. In this paper, we provide an overview of the next-generation artificial intelligence and blockchain technologies and present innovative solutions that may be used to accelerate the biomedical research and enable patients with new tools to control and profit from their personal data as well with the incentives to undergo constant health monitoring. We introduce new concepts to appraise and evaluate personal records, including the combination-, time- and relationship-value of the data. We also present a roadmap for a blockchain-enabled decentralized personal health data ecosystem to enable novel approaches for drug discovery, biomarker development, and preventative healthcare. A secure and transparent distributed personal data marketplace utilizing blockchain and deep learning technologies may be able to resolve the challenges faced by the regulators and return the control over personal data including medical records back to the individuals.
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    Zhavoronkov, A.; Zagribelnyy, B.; Zhebrak, A.; Aladinskiy, V.; Terentiev, V.; Vanhaelen, Q.; Bezrukov, D. S.; Polykovskiy, D.; Shayakhmetov, R.; Filimonov, A.; Filimonov, A.; Bishop, M.; McCloskey, S.; Lejia, E.; Bright, D.; Funakawa, K.; Lin, Y.-C.; Huang, S.-H.; Liao, H.-J.; Aliper, A.; Ivanenkov, Y. Potential non-covalent SARS-CoV-2 3C-like protease inhibitors designed using generative deep learning approaches and reviewed by human medicinal chemist in virtual reality. ChemRxiv , 2020.
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    Paul, D.; Sanap, G.; Shenoy, S.; Kalyane, D.; Kalia, K.; Tekade, R. K. Artificial intelligence in drug discovery and development. Drug Discovery Today 2021, 26, 80,  DOI: 10.1016/j.drudis.2020.10.010
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    Artificial intelligence in drug discovery and development
    Paul, Debleena; Sanap, Gaurav; Shenoy, Snehal; Kalyane, Dnyaneshwar; Kalia, Kiran; Tekade, Rakesh K.
    Drug Discovery Today (2021), 26 (1), 80-93CODEN: DDTOFS; ISSN:1359-6446. (Elsevier Ltd.)
    A review. Artificial Intelligence (AI) has recently started to gear-up its application in various sectors of the society with the pharmaceutical industry as a front-runner beneficiary. This review highlights the impactful use of AI in diverse areas of the pharmaceutical sectors viz., drug discovery and development, drug repurposing, improving pharmaceutical productivity, clin. trials, etc. to name a few, thus reducing the human workload as well as achieving targets in a short period. Crosstalk on the tools and techniques utilized in enforcing AI, ongoing challenges, and ways to overcome them, along with the future of AI in the pharmaceutical industry, is also discussed.
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    Martinelli, D. Generative machine learning for de novo drug discovery: A systematic review. Comput. Biol. Med. 2022, 145, 105403,  DOI: 10.1016/j.compbiomed.2022.105403
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    Generative machine learning for de novo drug discovery: A systematic review
    Martinelli Dominic D
    Computers in biology and medicine (2022), 145 (), 105403 ISSN:.
    Recent research on artificial intelligence indicates that machine learning algorithms can auto-generate novel drug-like molecules. Generative models have revolutionized de novo drug discovery, rendering the explorative process more efficient. Several model frameworks and input formats have been proposed to enhance the performance of intelligent algorithms in generative molecular design. In this systematic literature review of experimental articles and reviews over the last five years, machine learning models, challenges associated with computational molecule design along with proposed solutions, and molecular encoding methods are discussed. A query-based search of the PubMed, ScienceDirect, Springer, Wiley Online Library, arXiv, MDPI, bioRxiv, and IEEE Xplore databases yielded 87 studies. Twelve additional studies were identified via citation searching. Of the articles in which machine learning was implemented, six prominent algorithms were identified: long short-term memory recurrent neural networks (LSTM-RNNs), variational autoencoders (VAEs), generative adversarial networks (GANs), adversarial autoencoders (AAEs), evolutionary algorithms, and gated recurrent unit (GRU-RNNs). Furthermore, eight central challenges were designated: homogeneity of generated molecular libraries, deficient synthesizability, limited assay data, model interpretability, incapacity for multi-property optimization, incomparability, restricted molecule size, and uncertainty in model evaluation. Molecules were encoded either as strings, which were occasionally augmented using randomization, as 2D graphs, or as 3D graphs. Statistical analysis and visualization are performed to illustrate how approaches to machine learning in de novo drug design have evolved over the past five years. Finally, future opportunities and reservations are discussed.
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    Gao, K.; Nguyen, D. D.; Tu, M.; Wei, G.-W. Generative Network Complex for the Automated Generation of Drug-like Molecules. J. Chem. Inf. Model. 2020, 60, 5682– 5698,  DOI: 10.1021/acs.jcim.0c00599
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    Generative Network Complex for the Automated Generation of Drug-like Molecules
    Gao, Kaifu; Nguyen, Duc Duy; Tu, Meihua; Wei, Guo-Wei
    Journal of Chemical Information and Modeling (2020), 60 (12), 5682-5698CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    Current drug discovery is expensive and time-consuming. It remains a challenging task to create a wide variety of novel compds. that not only have desirable pharmacol. properties but also are cheaply available to low-income people. In this work, we develop a generative network complex (GNC) to generate new drug-like mols. based on the multiproperty optimization via the gradient descent in the latent space of an autoencoder. In our GNC, both multiple chem. properties and similarity scores are optimized to generate drug-like mols. with desired chem. properties. To further validate the reliability of the predictions, these mols. are reevaluated and screened by independent 2D fingerprint-based predictors to come up with a few hundreds of new drug candidates. As a demonstration, we apply our GNC to generate a large no. of new BACE1 inhibitors, as well as thousands of novel alternative drug candidates for eight existing market drugs, including Ceritinib, Ribociclib, Acalabrutinib, Idelalisib, Dabrafenib, Macimorelin, Enzalutamide, and Panobinostat.
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    Goodfellow, I.; Pouget-Abadie, J.; Mirza, M.; Xu, B.; Warde-Farley, D.; Ozair, S.; Courville, A.; Bengio, Y. Generative adversarial nets. In Advances in Neural Information Processing Systems 27 (NIPS 2014); Ghahramani, Z.; Welling, M.; Cortes, C.; Lawrence, N.; Weinberger, K. Q., Eds.; 2014.
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    Karras, T.; Aila, T.; Laine, S.; Lehtinen, J. Progressive growing of gans for improved quality, stability, and variation. arXiv preprint , 2017, arXiv:1710.10196.
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    Isola, P.; Zhu, J.-Y.; Zhou, T.; Efros, A. A. Image-to-image translation with conditional adversarial networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , 2017; pp 1125– 1134.
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    Zhu, J.-Y.; Park, T.; Isola, P.; Efros, A. A. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE International Conference on Computer Vision , 2017; pp 2223– 2232.
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    Karras, T.; Laine, S.; Aila, T. A style-based generator architecture for generative adversarial networks. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , 2019; pp 4401– 4410.
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    Jangid, D. K.; Brodnik, N. R.; Khan, A.; Goebel, M. G.; Echlin, M. P.; Pollock, T. M.; Daly, S. H.; Manjunath, B. 3D Grain Shape Generation in Polycrystals Using Generative Adversarial Networks. Integr. Mater. Manuf. Innov. 2022, 11, 71– 84,  DOI: 10.1007/s40192-021-00244-1
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    Kadurin, A.; Nikolenko, S.; Khrabrov, K.; Aliper, A.; Zhavoronkov, A. druGAN: an advanced generative adversarial autoencoder model for de novo generation of new molecules with desired molecular properties in silico. Mol. Pharmaceutics 2017, 14, 3098– 3104,  DOI: 10.1021/acs.molpharmaceut.7b00346
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    druGAN: An Advanced Generative Adversarial Autoencoder Model for de Novo Generation of New Molecules with Desired Molecular Properties in Silico
    Kadurin, Artur; Nikolenko, Sergey; Khrabrov, Kuzma; Aliper, Alex; Zhavoronkov, Alex
    Molecular Pharmaceutics (2017), 14 (9), 3098-3104CODEN: MPOHBP; ISSN:1543-8384. (American Chemical Society)
    Deep generative adversarial networks (GANs) are the emerging technol. in drug discovery and biomarker development. In our recent work, we demonstrated a proof-of-concept of implementing deep generative adversarial autoencoder (AAE) to identify new mol. fingerprints with predefined anticancer properties. Another popular generative model is the variational autoencoder (VAE), which is based on deep neural architectures. In this work, we developed an advanced AAE model for mol. feature extn. problems, and demonstrated its advantages compared to VAE in terms of (a) adjustability in generating mol. fingerprints; (b) capacity of processing very large mol. data sets; and (c) efficiency in unsupervised pretraining for regression model. Our results suggest that the proposed AAE model significantly enhances the capacity and efficiency of development of the new mols. with specific anticancer properties using the deep generative models.
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    Vanhaelen, Q.; Lin, Y.-C.; Zhavoronkov, A. The advent of generative chemistry. ACS Med. Chem. Lett. 2020, 11, 1496– 1505,  DOI: 10.1021/acsmedchemlett.0c00088
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    The Advent of Generative Chemistry
    Vanhaelen, Quentin; Lin, Yen-Chu; Zhavoronkov, Alex
    ACS Medicinal Chemistry Letters (2020), 11 (8), 1496-1505CODEN: AMCLCT; ISSN:1948-5875. (American Chemical Society)
    A review. Generative adversarial networks (GANs), first published in 2014, are among the most important concepts in modern artificial intelligence (AI). Bridging deep learning and game theory, GANs are used to generate or "imagine" new objects with desired properties. Since 2016, multiple GANs with reinforcement learning (RL) have been successfully applied in pharmacol. for de novo mol. design. Those techniques aim at a more efficient use of the data and a better exploration of the chem. space. We review recent advances for the generation of novel mols. with desired properties with a focus on the applications of GANs, RL, and related techniques. We also discuss the current limitations and challenges in the new growing field of generative chem.
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    Xu, M.; Cheng, J.; Liu, Y.; Huang, W. DeepGAN: Generating Molecule for Drug Discovery Based on Generative Adversarial Network. In 2021 IEEE Symposium on Computers and Communications (ISCC) , 2021; pp 1– 6.
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    Guimaraes, G. L.; Sanchez-Lengeling, B.; Outeiral, C.; Farias, P. L. C.; Aspuru-Guzik, A. Objective-reinforced generative adversarial networks (ORGAN) for sequence generation models. arXiv preprint , arXiv:1705.10843, 2017.
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    Yu, L.; Zhang, W.; Wang, J.; Yu, Y. SeqGAN: sequence generative adversarial nets with policy gradient. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence , 2017; pp 2852– 2858.
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    Prykhodko, O.; Johansson, S. V.; Kotsias, P.-C.; Arús-Pous, J.; Bjerrum, E. J.; Engkvist, O.; Chen, H. A de novo molecular generation method using latent vector based generative adversarial network. J. Cheminf. 2019, 11, 1– 13,  DOI: 10.1186/s13321-019-0397-9
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    Kotsias, P.-C.; Arús-Pous, J.; Chen, H.; Engkvist, O.; Tyrchan, C.; Bjerrum, E. J. Direct steering of de novo molecular generation with descriptor conditional recurrent neural networks. Nat. Mach. Intell. 2020, 2, 254– 265,  DOI: 10.1038/s42256-020-0174-5
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    De Cao, N.; Kipf, T. MolGAN: An implicit generative model for small molecular graphs. arXiv preprint arXiv:1805.11973 2018,.
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    Neukart, F.; Compostella, G.; Seidel, C.; Von Dollen, D.; Yarkoni, S.; Parney, B. Traffic flow optimization using a quantum annealer. Front. ICT 2017, 4, 29,  DOI: 10.3389/fict.2017.00029
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    Harwood, S.; Gambella, C.; Trenev, D.; Simonetto, A.; Bernal Neira, D.; Greenberg, D. Formulating and solving routing problems on quantum computers. IEEE Trans. Quantum Eng. 2021, 2, 1– 17,  DOI: 10.1109/TQE.2021.3049230
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    Orus, R.; Mugel, S.; Lizaso, E. Quantum computing for finance: Overview and prospects. Rev. Phys. 2019, 4, 100028,  DOI: 10.1016/j.revip.2019.100028
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    Liu, G.; Ma, W. A quantum artificial neural network for stock closing price prediction. Inf. Sci. (N.Y.) 2022, 598, 75– 85,  DOI: 10.1016/j.ins.2022.03.064
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    Du, Y.; Yang, Y.; Tao, D.; Hsieh, M.-H. Demystify Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification. arXiv preprint , arXiv:2301.01597, 2022.
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    Yin, X.-F.; Du, Y.; Fei, Y.-Y.; Zhang, R.; Liu, L.-Z.; Mao, Y.; Liu, T.; Hsieh, M.-H.; Li, L.; Liu, N.-L.; Tao, D.; Chen, Y.-A.; Pan, J.-W. Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver. Phys. Rev. Lett. 2022, 128, 110501,  DOI: 10.1103/PhysRevLett.128.110501
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    Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver
    Yin, Xu-Fei; Du, Yuxuan; Fei, Yue-Yang; Zhang, Rui; Liu, Li-Zheng; Mao, Yingqiu; Liu, Tongliang; Hsieh, Min-Hsiu; Li, Li; Liu, Nai-Le; Tao, Dacheng; Chen, Yu-Ao; Pan, Jian-Wei
    Physical Review Letters (2022), 128 (11), 110501CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits, where a two-outcome measurement can be used to query a classical binary result about whether the input state is bipartite entangled or not. In principle, for an N-qubit quantum state, the runtime complexity of our proposal is O(poly(N)T) with T being the no. of iterations. We exptl. implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states. Our work paves the way for using near-term quantum machines to tackle entanglement detection on multipartite entangled quantum systems.
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    Rudolph, M. S.; Toussaint, N. B.; Katabarwa, A.; Johri, S.; Peropadre, B.; Perdomo-Ortiz, A. Generation of high-resolution handwritten digits with an ion-trap quantum computer. Phys. Rev. X 2022, 12, 031010,  DOI: 10.1103/PhysRevX.12.031010
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    Generation of High-Resolution Handwritten Digits with an Ion-Trap Quantum Computer
    Rudolph, Manuel S.; Toussaint, Ntwali Bashige; Katabarwa, Amara; Johri, Sonika; Peropadre, Borja; Perdomo-Ortiz, Alejandro
    Physical Review X (2022), 12 (3), 031010CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    Generating high-quality data (e.g., images or video) is one of the most exciting and challenging frontiers in unsupervised machine learning. Utilizing quantum computers in such tasks to potentially enhance conventional machine-learning algorithms has emerged as a promising application but poses big challenges due to the limited no. of qubits and the level of gate noise in available devices. In this work, we provide the first practical and exptl. implementation of a quantum-classical generative algorithm capable of generating high-resoln. images of handwritten digits with state-of-the-art gate-based quantum computers. In our quantum-assisted machine-learning framework, we implement a quantum-circuit-based generative model to learn and sample the prior distribution of a generative adversarial network. We introduce a multibasis technique which leverages the unique possibility of measuring quantum states in different bases, hence enhancing the expressivity of the prior distribution. We train this hybrid algorithm on an ion-trap device based on Yb+171 ion qubits to generate high-quality images and quant. outperform comparable classical generative adversarial networks trained on the popular MNIST dataset for handwritten digits.
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    Aspuru-Guzik, A.; Dutoi, A. D.; Love, P. J.; Head-Gordon, M. Simulated quantum computation of molecular energies. Science 2005, 309, 1704– 1707,  DOI: 10.1126/science.1113479
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    Simulated Quantum Computation of Molecular Energies
    Aspuru-Guzik, Alan; Dutoi, Anthony D.; Love, Peter J.; Head-Gordon, Martin
    Science (Washington, DC, United States) (2005), 309 (5741), 1704-1707CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    The calcn. time for the energy of atoms and mols. scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chem. interest using modest nos. of quantum bits. Calcns. of the water and lithium hydride mol. ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estn. algorithm. The recursive algorithm reduces the no. of quantum bits required for the readout register from about 20 to 4. Mappings of the mol. wave function to the quantum bits are described. An adiabatic method for the prepn. of a good approx. ground-state wave function is described and demonstrated for a stretched hydrogen mol. The no. of quantum bits required scales linearly with the no. of basis functions, and the no. of gates required grows polynomially with the no. of quantum bits.
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    Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G.; Goggin, M. E.; Almeida, M. P.; Kassal, I.; Biamonte, J. D.; Mohseni, M.; Powell, B. J.; Barbieri, M.; Aspuru-Guzik, A.; White, A. G. Towards quantum chemistry on a quantum computer. Nat. Chem. 2010, 2, 106– 111,  DOI: 10.1038/nchem.483
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    Towards quantum chemistry on a quantum computer
    Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G.; Goggin, M. E.; Almeida, M. P.; Kassal, I.; Biamonte, J. D.; Mohseni, M.; Powell, B. J.; Barbieri, M.; Aspuru-Guzik, A.; White, A. G.
    Nature Chemistry (2010), 2 (2), 106-111CODEN: NCAHBB; ISSN:1755-4330. (Nature Publishing Group)
    Exact first-principles calcns. of mol. properties are currently intractable because their computational cost grows exponentially with both the no. of atoms and basis set size. A soln. is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technol. to calc. properties of the smallest mol. system: the mol. in a minimal basis. We calc. the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chem. problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chem. applications.
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    Peruzzo, A.; McClean, J.; Shadbolt, P.; Yung, M.-H.; Zhou, X.-Q.; Love, P. J.; Aspuru-Guzik, A.; O’brien, J. L. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 2014, 5, 1– 7,  DOI: 10.1038/ncomms5213
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    O’Malley, P. J. J.; Babbush, R.; Kivlichan, I. D.; Romero, J.; McClean, J. R.; Barends, R.; Kelly, J.; Roushan, P.; Tranter, A.; Ding, N.; Campbell, B.; Chen, Y.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fowler, A. G.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Coveney, P. V.; Love, P. J.; Neven, H.; Aspuru-Guzik, A.; Martinis, J. M. Scalable quantum simulation of molecular energies. Phys. Rev. X 2016, 6, 031007,  DOI: 10.1103/PhysRevX.6.031007
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    Scalable quantum simulation of molecular energies
    O'Malley, P. J. J.; Babbush, R.; Kivlichan, I. D.; Romero, J.; McClean, J. R.; Barends, R.; Kelly, J.; Roushan, P.; Tranter, A.; Ding, N.; Campbell, B.; Chen, Y.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fowler, A. G.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Coveney, P. V.; Love, P. J.; Neven, H.; Aspuru-Guzik, A.; Martinis, J. M.
    Physical Review X (2016), 6 (3), 031007/1-031007/13CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    We report the first electronic structure calcn. performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute the energy surface of mol. hydrogen using two distinct quantum algorithms. First, we exptl. execute the unitary coupled cluster method using the variational quantum eigensolver. Our efficient implementation predicts the correct dissocn. energy to within chem. accuracy of the numerically exact result. Second, we exptl. demonstrate the canonical quantum algorithm for chem., which consists of Trotterization and quantum phase estn. We compare the exptl. performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors. This error tolerance inspires hope that variational quantum simulations of classically intractable mols. may be viable in the near future.
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    Kandala, A.; Mezzacapo, A.; Temme, K.; Takita, M.; Brink, M.; Chow, J. M.; Gambetta, J. M. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 2017, 549, 242– 246,  DOI: 10.1038/nature23879
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    Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
    Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan; Takita, Maika; Brink, Markus; Chow, Jerry M.; Gambetta, Jay M.
    Nature (London, United Kingdom) (2017), 549 (7671), 242-246CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
    Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers. Finding exact solns. to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet exptl. implementations have so far been restricted to mols. involving only hydrogen and helium. Here we demonstrate the exptl. optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, detg. the ground-state energy for mols. of increasing size, up to BeH2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepd. trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our expts. and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.
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    Cao, Y.; Romero, J.; Olson, J. P.; Degroote, M.; Johnson, P. D.; Kieferová, M.; Kivlichan, I. D.; Menke, T.; Peropadre, B.; Sawaya, N. P. D.; Sim, S.; Veis, L.; Aspuru-Guzik, A. Quantum Chemistry in the Age of Quantum Computing. Chem. Rev. 2019, 119, 10856– 10915,  DOI: 10.1021/acs.chemrev.8b00803
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    Quantum Chemistry in the Age of Quantum Computing
    Cao, Yudong; Romero, Jonathan; Olson, Jonathan P.; Degroote, Matthias; Johnson, Peter D.; Kieferova, Maria; Kivlichan, Ian D.; Menke, Tim; Peropadre, Borja; Sawaya, Nicolas P. D.; Sim, Sukin; Veis, Libor; Aspuru-Guzik, Alan
    Chemical Reviews (Washington, DC, United States) (2019), 119 (19), 10856-10915CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chem. communities over the past century. Although many approxn. methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging complexity landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chem. such as the electronic structure of mols. In the past two decades significant advances have been made in developing algorithms and phys. hardware for quantum computing, heralding a revolution in simulation of quantum systems. This article is an overview of the algorithms and results that are relevant for quantum chem. The intended audience is both quantum chemists who seek to learn more about quantum computing, and quantum computing researchers who would like to explore applications in quantum chem.
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    Quantum, G. A.; Collaborators*†; Arute, F.; Arya, K.; Babbush, R.; Bacon, D.; Bardin, J. C.; Barends, R.; Boixo, S.; Broughton, M. Hartree-Fock on a superconducting qubit quantum computer. Science 2020, 369, 1084– 1089,  DOI: 10.1126/science.abb9811
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    Gao, Q.; Nakamura, H.; Gujarati, T. P.; Jones, G. O.; Rice, J. E.; Wood, S. P.; Pistoia, M.; Garcia, J. M.; Yamamoto, N. Computational investigations of the lithium superoxide dimer rearrangement on noisy quantum devices. J. Phys. Chem. A 2021, 125, 1827– 1836,  DOI: 10.1021/acs.jpca.0c09530
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    Computational Investigations of the Lithium Superoxide Dimer Rearrangement on Noisy Quantum Devices
    Gao, Qi; Nakamura, Hajime; Gujarati, Tanvi P.; Jones, Gavin O.; Rice, Julia E.; Wood, Stephen P.; Pistoia, Marco; Garcia, Jeannette M.; Yamamoto, Naoki
    Journal of Physical Chemistry A (2021), 125 (9), 1827-1836CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    Quantum chem. studies of biradical systems are challenging due to the required multiconfigurational nature of the wavefunction. In this work, Variational Quantum Eigensolver (VQE) is used to compute the energy profile for the lithium superoxide dimer rearrangement, involving biradical species, on quantum simulators and devices. Considering that current quantum devices can only handle limited no. of qubits, we present guidelines for selecting an appropriate active space to perform computations on chem. systems that require many qubits. We show that with VQE performed with a quantum simulator reproduces results obtained with full-CI (Full CI) for the chosen active space. However, results deviate from exact values by about 39 mHa for calcns. on a quantum device. This deviation can be improved to about 4 mHa using the readout mitigation approach and can be further improved to 2 mHa, approaching chem. accuracy, using the state tomog. technique to purify the calcd. quantum state.
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    Shee, Y.; Yeh, T.-L.; Hsiao, J.-Y.; Yang, A.; Lin, Y.-C.; Hsieh, M.-H. Quantum Simulation of Preferred Tautomeric State Prediction. arXiv preprint , arXiv:2210.02977, 2022.
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    Cao, Y.; Romero, J.; Aspuru-Guzik, A. Potential of quantum computing for drug discovery. IBM J. Res. Dev. 2018, 62, 1– 20,  DOI: 10.1147/JRD.2018.2888987
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    Li, J.; Topaloglu, R. O.; Ghosh, S. Quantum generative models for small molecule drug discovery. IEEE Trans. Quantum Eng. 2021, 2, 1– 8,  DOI: 10.1109/TQE.2021.3104804
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    Bharti, K.; Cervera-Lierta, A.; Kyaw, T. H.; Haug, T.; Alperin-Lea, S.; Anand, A.; Degroote, M.; Heimonen, H.; Kottmann, J. S.; Menke, T.; Mok, W.-K.; Sim, S.; Kwek, L.-C.; Aspuru-Guzik, A. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 2022, 94, 015004,  DOI: 10.1103/RevModPhys.94.015004
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    Noisy intermediate-scale quantum algorithms
    Bharti, Kishor; Cervera-Lierta, Alba; Kyaw, Thi Ha; Haug, Tobias; Alperin-Lea, Sumner; Anand, Abhinav; Degroote, Matthias; Heimonen, Hermanni; Kottmann, Jakob S.; Menke, Tim; Mok, Wai-Keong; Sim, Sukin; Kwek, Leong-Chuan; Aspuru-Guzik, Alan
    Reviews of Modern Physics (2022), 94 (1), 015004CODEN: RMPHAT; ISSN:1539-0756. (American Physical Society)
    A review. A universal fault-tolerant quantum computer that can efficiently solve problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the exptl. advancement toward realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e., qubits that are not error cor., and therefore perform imperfect operations within a limited coherence time. In the search for achieving quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chem., and combinatorial optimization. The overarching goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, a thorough summary of NISQ computational paradigms and algorithms is provided. The key structure of these algorithms and their limitations and advantages are discussed. A comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices is addnl. provided.
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    Du, Y.; Hsieh, M.-H.; Liu, T.; Tao, D. Expressive power of parametrized quantum circuits. Phys. Rev. Res. 2020, 2, 033125,  DOI: 10.1103/PhysRevResearch.2.033125
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    Expressive power of parametrized quantum circuits
    Du, Yuxuan; Hsieh, Min-Hsiu; Liu, Tongliang; Tao, Dacheng
    Physical Review Research (2020), 2 (3), 033125CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
    Parametrized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum polynomial circuits). In addn., PQCs equipped with ancillary qubits for postselection may possess expressive power stronger than that of those without postselection. We employ them as an application for Bayesian learning, since it is possible to learn prior probabilities rather than assuming they are known. We expect that it will find many more applications in semisupervised learning where prior distributions are normally assumed to be unknown. Lastly, we conduct several numerical expts. using the Rigetti Forest platform to demonstrate the performance of the proposed Bayesian quantum circuit.
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    Du, Y.; Hsieh, M.-H.; Liu, T.; You, S.; Tao, D. Learnability of quantum neural networks. PRX Quantum 2021, 2, 040337,  DOI: 10.1103/PRXQuantum.2.040337
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    Du, Y.; Hsieh, M.-H.; Liu, T.; Tao, D.; Liu, N. Quantum noise protects quantum classifiers against adversaries. Phys. Rev. Res. 2021, 3, 023153,  DOI: 10.1103/PhysRevResearch.3.023153
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    Quantum noise protects quantum classifiers against adversaries
    Du, Yuxuan; Hsieh, Min-Hsiu; Liu, Tongliang; Tao, Dacheng; Liu, Nana
    Physical Review Research (2021), 3 (2), 023153CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
    Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, esp. in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy. It is then natural to ask: Can we harness the power of quantum noise that is beneficial to quantum computing. An important current direction for quantum computing is its application to machine learning, such as classification problems. One outstanding problem in machine learning for classification is its sensitivity to adversarial examples. These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers. They can also be considered as worst-case perturbations by unknown noise sources. We show that by taking advantage of depolarization noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise. This robustness property is intimately connected with an important security concept called differential privacy, which can be extended to quantum differential privacy. For the protection of quantum data, this quantum protocol can be used against the most general adversaries. Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of the classification model are absent, thus also providing a potential quantum advantage for classical data. This opens the opportunity to explore other ways in which quantum noise can be used in our favor, as well as identifying other ways quantum algorithms can be helpful in a way which is distinct from quantum speedups.
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    Lloyd, S.; Weedbrook, C. Quantum generative adversarial learning. Phys. Rev. Lett. 2018, 121, 040502,  DOI: 10.1103/PhysRevLett.121.040502
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    Quantum Generative Adversarial Learning
    Lloyd, Seth; Weedbrook, Christian
    Physical Review Letters (2018), 121 (4), 040502CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Generative adversarial networks represent a powerful tool for classical machine learning: a generator tries to create statistics for data that mimics those of a true data set, while a discriminator tries to discriminate between the true and fake data. The learning process for generator and discriminator can be thought of as an adversarial game, and under reasonable assumptions, the game converges to the point where the generator generates the same statistics as the true data and the discriminator is unable to discriminate between the true and the generated data. This Letter introduces the notion of quantum generative adversarial networks, where the data consist either of quantum states or of classical data, and the generator and discriminator are equipped with quantum information processors. We show that the unique fixed point of the quantum adversarial game also occurs when the generator produces the same statistics as the data. Neither the generator nor the discriminator perform quantum tomog.; linear programing drives them to the optimal. Since quantum systems are intrinsically probabilistic, the proof of the quantum case is different from-and simpler than-the classical case. We show that, when the data consist of samples of measurements made on high-dimensional spaces, quantum adversarial networks may exhibit an exponential advantage over classical adversarial networks.
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    Huang, H.-L.; Du, Y.; Gong, M.; Zhao, Y.; Wu, Y.; Wang, C.; Li, S.; Liang, F.; Lin, J.; Xu, Y.; Yang, R.; Liu, T.; Hsieh, M.-H.; Deng, H.; Rong, H.; Peng, C.-Z.; Lu, C.-Y.; Chen, Y.-A.; Tao, D.; Zhu, X.; Pan, J.-W. Experimental quantum generative adversarial networks for image generation. Phys. Rev. Appl. 2021, 16, 024051,  DOI: 10.1103/PhysRevApplied.16.024051
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    Experimental Quantum Generative Adversarial Networks for Image Generation
    Huang, He-Liang; Du, Yuxuan; Gong, Ming; Zhao, Youwei; Wu, Yulin; Wang, Chaoyue; Li, Shaowei; Liang, Futian; Lin, Jin; Xu, Yu; Yang, Rui; Liu, Tongliang; Hsieh, Min-Hsiu; Deng, Hui; Rong, Hao; Peng, Cheng-Zhi; Lu, Chao-Yang; Chen, Yu-Ao; Tao, Dacheng; Zhu, Xiaobo; Pan, Jian-Wei
    Physical Review Applied (2021), 16 (2), 024051CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
    Quantum machine learning is expected to be one of the first practical applications of near-term quantum devices. Pioneer theor. works suggest that quantum generative adversarial networks (GANs) may exhibit a potential exponential advantage over classical GANs, thus attracting widespread attention. However, it remains elusive whether quantum GANs implemented on near-term quantum devices can actually solve real-world learning tasks. Here, we devise a flexible quantum GAN scheme to narrow this knowledge gap. In principle, this scheme has the ability to complete image generation with high-dimensional features and could harness quantum superposition to train multiple examples in parallel. We exptl. achieve the learning and generating of real-world handwritten digit images on a superconducting quantum processor. Moreover, we utilize a gray-scale bar dataset to exhibit competitive performance between quantum GANs and the classical GANs based on multilayer perceptron and convolutional neural network architectures, resp., benchmarked by the Fr´echet distance score. Our work provides guidance for developing advanced quantum generative models on near-term quantum devices and opens up an avenue for exploring quantum advantages in various GAN-related learning tasks.
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    Dallaire-Demers, P.-L.; Killoran, N. Quantum generative adversarial networks. Phys. Rev. A 2018, 98, 012324,  DOI: 10.1103/PhysRevA.98.012324
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    Quantum generative adversarial networks
    Dallaire-Demers, Pierre-Luc; Killoran, Nathan
    Physical Review A (2018), 98 (1), 012324CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
    Quantum machine learning is expected to be one of the first potential general-purpose applications of near-term quantum devices. A major recent breakthrough in classical machine learning is the notion of generative adversarial training, where the gradients of a discriminator model are used to train a sep. generative model. In this work and a companion paper, we extend adversarial training to the quantum domain and show how to construct generative adversarial networks using quantum circuits. Furthermore, we also show how to compute gradients-a key element in generative adversarial network training-using another quantum circuit. We give an example of a simple practical circuit ansatz to parametrize quantum machine learning models and perform a simple numerical expt. to demonstrate that quantum generative adversarial networks can be trained successfully.
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    Romero, J.; Aspuru-Guzik, A. Variational quantum generators: Generative adversarial quantum machine learning for continuous distributions. Adv. Quantum Technol. 2021, 4, 2000003,  DOI: 10.1002/qute.202000003
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    Li, J. Quantum GAN with Hybrid Generator. https://github.com/jundeli/quantum-gan, accessed Aug. 2, 2021.
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    Ivanenkov, Y. A.; Polykovskiy, D.; Bezrukov, D.; Zagribelnyy, B.; Aladinskiy, V.; Kamya, P.; Aliper, A.; Ren, F.; Zhavoronkov, A. Chemistry42: An AI-Driven Platform for Molecular Design and Optimization. J. Chem. Inf. Model. 2023, 63, 695– 701,  DOI: 10.1021/acs.jcim.2c01191
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    Chemistry42: An AI-Driven Platform for Molecular Design and Optimization
    Ivanenkov, Yan A.; Polykovskiy, Daniil; Bezrukov, Dmitry; Zagribelnyy, Bogdan; Aladinskiy, Vladimir; Kamya, Petrina; Aliper, Alex; Ren, Feng; Zhavoronkov, Alex
    Journal of Chemical Information and Modeling (2023), 63 (3), 695-701CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    Chem.42 is a software platform for de novo small mol. design and optimization that integrates Artificial Intelligence (AI) techniques with computational and medicinal chem. methodologies. Chem.42 efficiently generates novel mol. structures with optimized properties validated in both in vitro and in vivo studies and is available through licensing or collaboration. Chem.42 is the core component of Insilico Medicine's Pharma.ai drug discovery suite. Pharma.ai also includes PandaOmics for target discovery and multiomics data anal., and inClinico-a data-driven multimodal forecast of a clin. trial's probability of success (PoS). In this paper, we demonstrate how the platform can be used to efficiently find novel mol. structures against DDR1 and CDK20.
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    Bergholm, V.; Izaac, J.; Schuld, M.; Gogolin, C.; Ahmed, S.; Ajith, V.; Alam, M. S.; Alonso-Linaje, G.; AkashNarayanan, B.; Asadi, A.; Arrazola, J. M.; Azad, U.; Banning, S.; Blank, C.; Bromley, T. R.; Cordier, B. A.; Ceroni, J.; Delgado, A.; Di Matteo, O.; Dusko, A.; Garg, T.; Guala, D.; Hayes, A.; Hill, R.; Ijaz, A.; Isacsson, T.; Ittah, D.; Jahangiri, S.; Jain, P.; Jiang, E.; Khandelwal, A.; Kottmann, K.; Lang, R. A.; Lee, C.; Loke, T.; Lowe, A.; McKiernan, K.; Meyer, J. J.; Montañez-Barrera, J. A.; Moyard, R.; Niu, Z.; O’Riordan, L. J.; Oud, S.; Panigrahi, A.; Park, C.-Y.; Polatajko, D.; Quesada, N.; Roberts, C.; Sá, N.; Schoch, I.; Shi, B.; Shu, S.; Sim, S.; Singh, A.; Strandberg, I.; Soni, J.; Száva, A.; Thabet, S.; Vargas-Hernández, R. A.; Vincent, T.; Vitucci, N.; Weber, M.; Wierichs, D.; Wiersema, R.; Willmann, M.; Wong, V.; Zhang, S.; Killoran, N. Pennylane: Automatic differentiation of hybrid quantum-classical computations. arXiv preprint , arXiv:1811.04968, 2018.
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    Arjovsky, M.; Chintala, S.; Bottou, L. Wasserstein generative adversarial networks. In International Conference on Machine Learning , 2017; pp 214 223.
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    Brown, N.; Fiscato, M.; Segler, M. H.; Vaucher, A. C. GuacaMol: benchmarking models for de novo molecular design. J. Chem. Inf. Model. 2019, 59, 1096– 1108,  DOI: 10.1021/acs.jcim.8b00839
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    GuacaMol: Benchmarking Models for de Novo Molecular Design
    Brown, Nathan; Fiscato, Marco; Segler, Marwin H. S.; Vaucher, Alain C.
    Journal of Chemical Information and Modeling (2019), 59 (3), 1096-1108CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    De novo design seeks to generate mols. with required property profiles by virtual design-make-test cycles. With the emergence of deep learning and neural generative models in many application areas, models for mol. design based on neural networks appeared recently and show promising results. However, the new models have not been profiled on consistent tasks, and comparative studies to well-established algorithms have only seldom been performed. To standardize the assessment of both classical and neural models for de novo mol. design, we propose an evaluation framework, GuacaMol, based on a suite of standardized benchmarks. The benchmark tasks encompass measuring the fidelity of the models to reproduce the property distribution of the training sets, the ability to generate novel mols., the exploration and exploitation of chem. space, and a variety of single and multiobjective optimization tasks. The benchmarking open-source Python code and a leaderboard can be found on https://benevolent.ai/guacamol.
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    Kaelbling, L. P.; Littman, M. L.; Moore, A. W. Reinforcement learning: A survey. J. Artif. Intell. Res. 1996, 4, 237– 285,  DOI: 10.1613/jair.301
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    Samanta, B.; De, A.; Ganguly, N.; Gomez-Rodriguez, M. Designing random graph models using variational autoencoders with applications to chemical design. arXiv preprint , arXiv:1802.05283, 2018.
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    Polykovskiy, D.; Zhebrak, A.; Sanchez-Lengeling, B.; Golovanov, S.; Tatanov, O.; Belyaev, S.; Kurbanov, R.; Artamonov, A.; Aladinskiy, V.; Veselov, M.; Kadurin, A.; Johansson, S.; Chen, H.; Nikolenko, S.; Aspuru-Guzik, A.; Zhavoronkov, A. Molecular sets (MOSES): a benchmarking platform for molecular generation models. Front. Pharmacol. 2020, 11, 565644,  DOI: 10.3389/fphar.2020.565644
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    Molecular sets (MOSES): a benchmarking platform for molecular generation models
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  • Abstract

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    Figure 1

    Figure 1. Overall pipeline. (a) The overall pipeline of MolGAN with different combinations of classical/quantum components. The reward neural network branch is enabled in the goal-directed benchmark. The classical noise generator samples from the Gaussian distribution, and the quantum one uses the variational quantum circuit (VQC). The classical generator is built by neural networks, and the quantum one uses the patch-based VQC to generate the molecular graph. The molecular graph is represented by a bond matrix and atom vector. The classical discriminator is built by a graph-based neural network or multilayer perceptron (MLP), and the VQC is used in the quantum one. (b) The example of VQC in the noise generator. (c) The patch method uses multiple VQCs as subgenerators. Each subgenerator takes noise as input and outputs a partial part of the final molecular graph. The final molecular graph is constructed by concatenating all the partial patches together. (d) The example of VQC in the quantum generator. (e) The VQC of the quantum discriminator consists of the amplitude embedding circuit (Sx), the strong entanglement layers (Uθ), and the measurement. (f) The VQC of strongly entanglement layers contains multiple CNOT gates and parametrized rotational gates (R). (g) MLP-based discriminator architecture in MolGAN-CC.

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    Figure 2

    Figure 2. Property distributions of molecules. (a) Drug properties distributions (left to right: QED, SA, and Solute) from valid and unique MolGAN-generated (in blue) and QuMolGAN-generated (in orange) molecules. (b) KL-divergence distributions (left to right: MolLogP, BertzCT, and MolWt) of valid and unique MolGAN-generated (blue), QuMolGAN-generated (orange), and QM9 (gray) molecules. (c) KL-divergence distributions (from left to right: MolLogP, BertzCT, and MolWt) of MolGAN-CC-ER-generated (orange), MolGAN-CQ-generated (yellow), MolGAN-generated (blue), and QM9 (gray) molecules.

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    Figure 3

    Figure 3. Example molecules. (a) Example molecules of MolGAN with z_dim = 2. (b) Example molecules of QuMolGAN with z_dim = 2. (c) Example molecules of MolGAN-CQ.

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      Kadurin Artur; Khrabrov Kuzma; Kadurin Artur; Aliper Alexander; Kazennov Andrey; Mamoshina Polina; Vanhaelen Quentin; Zhavoronkov Alex; Kadurin Artur; Kadurin Artur; Kazennov Andrey; Zhavoronkov Alex; Mamoshina Polina; Zhavoronkov Alex
      Oncotarget (2017), 8 (7), 10883-10890 ISSN:.
      Recent advances in deep learning and specifically in generative adversarial networks have demonstrated surprising results in generating new images and videos upon request even using natural language as input. In this paper we present the first application of generative adversarial autoencoders (AAE) for generating novel molecular fingerprints with a defined set of parameters. We developed a 7-layer AAE architecture with the latent middle layer serving as a discriminator. As an input and output the AAE uses a vector of binary fingerprints and concentration of the molecule. In the latent layer we also introduced a neuron responsible for growth inhibition percentage, which when negative indicates the reduction in the number of tumor cells after the treatment. To train the AAE we used the NCI-60 cell line assay data for 6252 compounds profiled on MCF-7 cell line. The output of the AAE was used to screen 72 million compounds in PubChem and select candidate molecules with potential anti-cancer properties. This approach is a proof of concept of an artificially-intelligent drug discovery engine, where AAEs are used to generate new molecular fingerprints with the desired molecular properties.
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    6. 6
      Zhavoronkov, A. Artificial intelligence for drug discovery, biomarker development, and generation of novel chemistry. Mol. Pharmaceutics 2018, 15, 4311,  DOI: 10.1021/acs.molpharmaceut.8b00930
      6
      Artificial Intelligence for Drug Discovery, Biomarker Development, and Generation of Novel Chemistry
      Zhavoronkov, Alex
      Molecular Pharmaceutics (2018), 15 (10), 4311-4313CODEN: MPOHBP; ISSN:1543-8384. (American Chemical Society)
      The potential of artificial intelligence in drug discovery is discussed and reviewed.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhslOgtrjE&md5=2c51295d4e682eeaf8069eddc09ed3e8
    7. 7
      Carracedo-Reboredo, P.; Liñares-Blanco, J.; Rodríguez-Fernández, N.; Cedrón, F.; Novoa, F. J.; Carballal, A.; Maojo, V.; Pazos, A.; Fernandez-Lozano, C. A review on machine learning approaches and trends in drug discovery. Comput. Struct. Biotechnol. J. 2021, 19, 4538– 4558,  DOI: 10.1016/j.csbj.2021.08.011
      7
      A review on machine learning approaches and trends in drug discovery
      Carracedo-Reboredo, Paula; Linares-Blanco, Jose; Rodriguez-Fernandez, Nereida; Cedron, Francisco; Novoa, Francisco J.; Carballal, Adrian; Maojo, Victor; Pazos, Alejandro; Fernandez-Lozano, Carlos
      Computational and Structural Biotechnology Journal (2021), 19 (), 4538-4558CODEN: CSBJAC; ISSN:2001-0370. (Elsevier B.V.)
      A review. Drug discovery aims at finding new compds. with specific chem. properties for the treatment of diseases. In the last years, the approach used in this search presents an important component in computer science with the skyrocketing of machine learning techniques due to its democratization. With the objectives set by the Precision Medicine initiative and the new challenges generated, it is necessary to establish robust, std. and reproducible computational methodologies to achieve the objectives set. Currently, predictive models based on Machine Learning have gained great importance in the step prior to preclin. studies. This stage manages to drastically reduce costs and research times in the discovery of new drugs. This review article focuses on how these new methodologies are being used in recent years of research. Analyzing the state of the art in this field will give us an idea of where cheminformatics will be developed in the short term, the limitations it presents and the pos. results it has achieved. This review will focus mainly on the methods used to model the mol. data, as well as the biol. problems addressed and the Machine Learning algorithms used for drug discovery in recent years.
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    8. 8
      Kao, P.-Y.; Kao, S.-M.; Huang, N.-L.; Lin, Y.-C. Toward Drug-Target Interaction Prediction via Ensemble Modeling and Transfer Learning. In 2021 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) , 2021; pp 2384– 2391.
      There is no corresponding record for this reference.
    9. 9
      Kolluri, S.; Lin, J.; Liu, R.; Zhang, Y.; Zhang, W. Machine Learning and Artificial Intelligence in Pharmaceutical Research and Development: a Review. AAPS J. 2022, 24, 1– 10,  DOI: 10.1208/s12248-021-00644-3
      There is no corresponding record for this reference.
    10. 10
      Zhavoronkov, A.; Ivanenkov, Y. A.; Aliper, A.; Veselov, M. S.; Aladinskiy, V. A.; Aladinskaya, A. V.; Terentiev, V. A.; Polykovskiy, D. A.; Kuznetsov, M. D.; Asadulaev, A.; Volkov, Y.; Zholus, A.; Shayakhmetov, R. R.; Zhebrak, A.; Minaeva, L. I.; Zagribelnyy, B. A.; Lee, L. H.; Soll, R.; Madge, D.; Xing, L.; Guo, T.; Aspuru-Guzik, A. Deep learning enables rapid identification of potent DDR1 kinase inhibitors. Nat. Biotechnol. 2019, 37, 1038– 1040,  DOI: 10.1038/s41587-019-0224-x
      10
      Deep learning enables rapid identification of potent DDR1 kinase inhibitors
      Zhavoronkov, Alex; Ivanenkov, Yan A.; Aliper, Alex; Veselov, Mark S.; Aladinskiy, Vladimir A.; Aladinskaya, Anastasiya V.; Terentiev, Victor A.; Polykovskiy, Daniil A.; Kuznetsov, Maksim D.; Asadulaev, Arip; Volkov, Yury; Zholus, Artem; Shayakhmetov, Rim R.; Zhebrak, Alexander; Minaeva, Lidiya I.; Zagribelnyy, Bogdan A.; Lee, Lennart H.; Soll, Richard; Madge, David; Xing, Li; Guo, Tao; Aspuru-Guzik, Alan
      Nature Biotechnology (2019), 37 (9), 1038-1040CODEN: NABIF9; ISSN:1087-0156. (Nature Research)
      We have developed a deep generative model, generative tensorial reinforcement learning (GENTRL), for de novo small-mol. design. GENTRL optimizes synthetic feasibility, novelty, and biol. activity. We used GENTRL to discover potent inhibitors of discoidin domain receptor 1 (DDR1), a kinase target implicated in fibrosis and other diseases, in 21 days. Four compds. were active in biochem. assays, and two were validated in cell-based assays. One lead candidate was tested and demonstrated favorable pharmacokinetics in mice.
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    11. 11
      Chan, H. S.; Shan, H.; Dahoun, T.; Vogel, H.; Yuan, S. Advancing drug discovery via artificial intelligence. Trends Pharmacol. Sci. 2019, 40, 592– 604,  DOI: 10.1016/j.tips.2019.06.004
      11
      Advancing Drug Discovery via Artificial Intelligence
      Chan, H. C. Stephen; Shan, Hanbin; Dahoun, Thamani; Vogel, Horst; Yuan, Shuguang
      Trends in Pharmacological Sciences (2019), 40 (8), 592-604CODEN: TPHSDY; ISSN:0165-6147. (Elsevier Ltd.)
      Drug discovery and development are among the most important translational science activities that contribute to human health and wellbeing. However, the development of a new drug is a very complex, expensive, and long process which typically costs 2.6 billion USD and takes 12 years on av. How to decrease the costs and speed up new drug discovery has become a challenging and urgent question in industry. Artificial intelligence (AI) combined with new exptl. technologies is expected to make the hunt for new pharmaceuticals quicker, cheaper, and more effective. We discuss here emerging applications of AI to improve the drug discovery process.
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    12. 12
      Schneider, G.; Fechner, U. Computer-based de novo design of drug-like molecules. Nat. Rev. Drug Discovery 2005, 4, 649– 663,  DOI: 10.1038/nrd1799
      12
      Computer-based de novo design of drug-like molecules
      Schneider, Gisbert; Fechner, Uli
      Nature Reviews Drug Discovery (2005), 4 (8), 649-663CODEN: NRDDAG; ISSN:1474-1776. (Nature Publishing Group)
      A review with refs. Ever since the first automated de novo design techniques were conceived only 15 years ago, the computer-based design of hit and lead structure candidates has emerged as a complementary approach to high-throughput screening. Although many challenges remain, de novo design supports drug discovery projects by generating novel pharmaceutically active agents with desired properties in a cost- and time-efficient manner. In this review, we outline the various design concepts and highlight current developments in computer-based de novo design.
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    13. 13
      Fischer, T.; Gazzola, S.; Riedl, R. Approaching target selectivity by de novo drug design. Expert Opin. Drug Discovery 2019, 14, 791– 803,  DOI: 10.1080/17460441.2019.1615435
      13
      Approaching Target Selectivity by De Novo Drug Design
      Fischer, Thomas; Gazzola, Silvia; Riedl, Rainer
      Expert Opinion on Drug Discovery (2019), 14 (8), 791-803CODEN: EODDBX; ISSN:1746-0441. (Taylor & Francis Ltd.)
      A review. The development of drug candidates with a defined selectivity profile and a unique mol. structure is of fundamental interest for drug discovery. In contrast to the costly screening of large substance libraries, the targeted de novo design of a drug by using structural information of either the biol. target and/or structure-activity relationship data of active modulators offers an efficient and intellectually appealing alternative.: This review provides an overview on the different techniques of de novo drug design (ligand-based drug design, structure-based drug design, and fragment-based drug design) and highlights successful examples of this targeted approach toward selective modulators of therapeutically relevant targets.: De novo drug design has established itself as a very efficient method for the development of potent and selective modulators for a variety of different biol. target classes. The ever-growing wealth of structural data on therapeutic targets will certainly further enhance the importance of de novo design for the drug discovery process in the future. However, a consistent use of the terminol. of de novo drug design in the scientific literature should be sought.
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    14. 14
      Mouchlis, V. D.; Afantitis, A.; Serra, A.; Fratello, M.; Papadiamantis, A. G.; Aidinis, V.; Lynch, I.; Greco, D.; Melagraki, G. Advances in de novo drug design: from conventional to machine learning methods. Int. J. Mol. Sci. 2021, 22, 1676,  DOI: 10.3390/ijms22041676
      There is no corresponding record for this reference.
    15. 15
      Speck-Planche, A. Recent advances in fragment-based computational drug design: tackling simultaneous targets/biological effects. Future Med. Chem. 2018, 10, 2021– 2024,  DOI: 10.4155/fmc-2018-0213
      15
      Recent advances in fragment-based computational drug design: tackling simultaneous targets/biological effects
      Speck-Planche, Alejandro
      Future Medicinal Chemistry (2018), 10 (17), 2021-2024CODEN: FMCUA7; ISSN:1756-8919. (Future Science Ltd.)
      There is no expanded citation for this reference.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhsF2gsLzJ&md5=a6a28a9e6dde2e290064bdf0f646b7e1
    16. 16
      Mamoshina, P.; Ojomoko, L.; Yanovich, Y.; Ostrovski, A.; Botezatu, A.; Prikhodko, P.; Izumchenko, E.; Aliper, A.; Romantsov, K.; Zhebrak, A.; Ogu, I. O.; Zhavoronkov, A. Converging blockchain and next-generation artificial intelligence technologies to decentralize and accelerate biomedical research and healthcare. Oncotarget 2018, 9, 5665,  DOI: 10.18632/oncotarget.22345
      16
      Converging blockchain and next-generation artificial intelligence technologies to decentralize and accelerate biomedical research and healthcare
      Mamoshina Polina; Ojomoko Lucy; Aliper Alexander; Romantsov Konstantin; Zhebrak Alexander; Zhavoronkov Alex; Mamoshina Polina; Yanovich Yury; Ostrovski Alex; Botezatu Alex; Prikhodko Pavel; Izumchenko Eugene; Ogu Iraneus Obioma; Zhavoronkov Alex
      Oncotarget (2018), 9 (5), 5665-5690 ISSN:.
      The increased availability of data and recent advancements in artificial intelligence present the unprecedented opportunities in healthcare and major challenges for the patients, developers, providers and regulators. The novel deep learning and transfer learning techniques are turning any data about the person into medical data transforming simple facial pictures and videos into powerful sources of data for predictive analytics. Presently, the patients do not have control over the access privileges to their medical records and remain unaware of the true value of the data they have. In this paper, we provide an overview of the next-generation artificial intelligence and blockchain technologies and present innovative solutions that may be used to accelerate the biomedical research and enable patients with new tools to control and profit from their personal data as well with the incentives to undergo constant health monitoring. We introduce new concepts to appraise and evaluate personal records, including the combination-, time- and relationship-value of the data. We also present a roadmap for a blockchain-enabled decentralized personal health data ecosystem to enable novel approaches for drug discovery, biomarker development, and preventative healthcare. A secure and transparent distributed personal data marketplace utilizing blockchain and deep learning technologies may be able to resolve the challenges faced by the regulators and return the control over personal data including medical records back to the individuals.
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    17. 17
      Zhavoronkov, A.; Zagribelnyy, B.; Zhebrak, A.; Aladinskiy, V.; Terentiev, V.; Vanhaelen, Q.; Bezrukov, D. S.; Polykovskiy, D.; Shayakhmetov, R.; Filimonov, A.; Filimonov, A.; Bishop, M.; McCloskey, S.; Lejia, E.; Bright, D.; Funakawa, K.; Lin, Y.-C.; Huang, S.-H.; Liao, H.-J.; Aliper, A.; Ivanenkov, Y. Potential non-covalent SARS-CoV-2 3C-like protease inhibitors designed using generative deep learning approaches and reviewed by human medicinal chemist in virtual reality. ChemRxiv , 2020.
      There is no corresponding record for this reference.
    18. 18
      Paul, D.; Sanap, G.; Shenoy, S.; Kalyane, D.; Kalia, K.; Tekade, R. K. Artificial intelligence in drug discovery and development. Drug Discovery Today 2021, 26, 80,  DOI: 10.1016/j.drudis.2020.10.010
      18
      Artificial intelligence in drug discovery and development
      Paul, Debleena; Sanap, Gaurav; Shenoy, Snehal; Kalyane, Dnyaneshwar; Kalia, Kiran; Tekade, Rakesh K.
      Drug Discovery Today (2021), 26 (1), 80-93CODEN: DDTOFS; ISSN:1359-6446. (Elsevier Ltd.)
      A review. Artificial Intelligence (AI) has recently started to gear-up its application in various sectors of the society with the pharmaceutical industry as a front-runner beneficiary. This review highlights the impactful use of AI in diverse areas of the pharmaceutical sectors viz., drug discovery and development, drug repurposing, improving pharmaceutical productivity, clin. trials, etc. to name a few, thus reducing the human workload as well as achieving targets in a short period. Crosstalk on the tools and techniques utilized in enforcing AI, ongoing challenges, and ways to overcome them, along with the future of AI in the pharmaceutical industry, is also discussed.
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    19. 19
      Martinelli, D. Generative machine learning for de novo drug discovery: A systematic review. Comput. Biol. Med. 2022, 145, 105403,  DOI: 10.1016/j.compbiomed.2022.105403
      19
      Generative machine learning for de novo drug discovery: A systematic review
      Martinelli Dominic D
      Computers in biology and medicine (2022), 145 (), 105403 ISSN:.
      Recent research on artificial intelligence indicates that machine learning algorithms can auto-generate novel drug-like molecules. Generative models have revolutionized de novo drug discovery, rendering the explorative process more efficient. Several model frameworks and input formats have been proposed to enhance the performance of intelligent algorithms in generative molecular design. In this systematic literature review of experimental articles and reviews over the last five years, machine learning models, challenges associated with computational molecule design along with proposed solutions, and molecular encoding methods are discussed. A query-based search of the PubMed, ScienceDirect, Springer, Wiley Online Library, arXiv, MDPI, bioRxiv, and IEEE Xplore databases yielded 87 studies. Twelve additional studies were identified via citation searching. Of the articles in which machine learning was implemented, six prominent algorithms were identified: long short-term memory recurrent neural networks (LSTM-RNNs), variational autoencoders (VAEs), generative adversarial networks (GANs), adversarial autoencoders (AAEs), evolutionary algorithms, and gated recurrent unit (GRU-RNNs). Furthermore, eight central challenges were designated: homogeneity of generated molecular libraries, deficient synthesizability, limited assay data, model interpretability, incapacity for multi-property optimization, incomparability, restricted molecule size, and uncertainty in model evaluation. Molecules were encoded either as strings, which were occasionally augmented using randomization, as 2D graphs, or as 3D graphs. Statistical analysis and visualization are performed to illustrate how approaches to machine learning in de novo drug design have evolved over the past five years. Finally, future opportunities and reservations are discussed.
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    20. 20
      Gao, K.; Nguyen, D. D.; Tu, M.; Wei, G.-W. Generative Network Complex for the Automated Generation of Drug-like Molecules. J. Chem. Inf. Model. 2020, 60, 5682– 5698,  DOI: 10.1021/acs.jcim.0c00599
      20
      Generative Network Complex for the Automated Generation of Drug-like Molecules
      Gao, Kaifu; Nguyen, Duc Duy; Tu, Meihua; Wei, Guo-Wei
      Journal of Chemical Information and Modeling (2020), 60 (12), 5682-5698CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Current drug discovery is expensive and time-consuming. It remains a challenging task to create a wide variety of novel compds. that not only have desirable pharmacol. properties but also are cheaply available to low-income people. In this work, we develop a generative network complex (GNC) to generate new drug-like mols. based on the multiproperty optimization via the gradient descent in the latent space of an autoencoder. In our GNC, both multiple chem. properties and similarity scores are optimized to generate drug-like mols. with desired chem. properties. To further validate the reliability of the predictions, these mols. are reevaluated and screened by independent 2D fingerprint-based predictors to come up with a few hundreds of new drug candidates. As a demonstration, we apply our GNC to generate a large no. of new BACE1 inhibitors, as well as thousands of novel alternative drug candidates for eight existing market drugs, including Ceritinib, Ribociclib, Acalabrutinib, Idelalisib, Dabrafenib, Macimorelin, Enzalutamide, and Panobinostat.
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    21. 21
      Goodfellow, I.; Pouget-Abadie, J.; Mirza, M.; Xu, B.; Warde-Farley, D.; Ozair, S.; Courville, A.; Bengio, Y. Generative adversarial nets. In Advances in Neural Information Processing Systems 27 (NIPS 2014); Ghahramani, Z.; Welling, M.; Cortes, C.; Lawrence, N.; Weinberger, K. Q., Eds.; 2014.
      There is no corresponding record for this reference.
    22. 22
      Karras, T.; Aila, T.; Laine, S.; Lehtinen, J. Progressive growing of gans for improved quality, stability, and variation. arXiv preprint , 2017, arXiv:1710.10196.
      There is no corresponding record for this reference.
    23. 23
      Isola, P.; Zhu, J.-Y.; Zhou, T.; Efros, A. A. Image-to-image translation with conditional adversarial networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , 2017; pp 1125– 1134.
      There is no corresponding record for this reference.
    24. 24
      Zhu, J.-Y.; Park, T.; Isola, P.; Efros, A. A. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE International Conference on Computer Vision , 2017; pp 2223– 2232.
      There is no corresponding record for this reference.
    25. 25
      Karras, T.; Laine, S.; Aila, T. A style-based generator architecture for generative adversarial networks. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , 2019; pp 4401– 4410.
      There is no corresponding record for this reference.
    26. 26
      Jangid, D. K.; Brodnik, N. R.; Khan, A.; Goebel, M. G.; Echlin, M. P.; Pollock, T. M.; Daly, S. H.; Manjunath, B. 3D Grain Shape Generation in Polycrystals Using Generative Adversarial Networks. Integr. Mater. Manuf. Innov. 2022, 11, 71– 84,  DOI: 10.1007/s40192-021-00244-1
      There is no corresponding record for this reference.
    27. 27
      Kadurin, A.; Nikolenko, S.; Khrabrov, K.; Aliper, A.; Zhavoronkov, A. druGAN: an advanced generative adversarial autoencoder model for de novo generation of new molecules with desired molecular properties in silico. Mol. Pharmaceutics 2017, 14, 3098– 3104,  DOI: 10.1021/acs.molpharmaceut.7b00346
      27
      druGAN: An Advanced Generative Adversarial Autoencoder Model for de Novo Generation of New Molecules with Desired Molecular Properties in Silico
      Kadurin, Artur; Nikolenko, Sergey; Khrabrov, Kuzma; Aliper, Alex; Zhavoronkov, Alex
      Molecular Pharmaceutics (2017), 14 (9), 3098-3104CODEN: MPOHBP; ISSN:1543-8384. (American Chemical Society)
      Deep generative adversarial networks (GANs) are the emerging technol. in drug discovery and biomarker development. In our recent work, we demonstrated a proof-of-concept of implementing deep generative adversarial autoencoder (AAE) to identify new mol. fingerprints with predefined anticancer properties. Another popular generative model is the variational autoencoder (VAE), which is based on deep neural architectures. In this work, we developed an advanced AAE model for mol. feature extn. problems, and demonstrated its advantages compared to VAE in terms of (a) adjustability in generating mol. fingerprints; (b) capacity of processing very large mol. data sets; and (c) efficiency in unsupervised pretraining for regression model. Our results suggest that the proposed AAE model significantly enhances the capacity and efficiency of development of the new mols. with specific anticancer properties using the deep generative models.
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    28. 28
      Vanhaelen, Q.; Lin, Y.-C.; Zhavoronkov, A. The advent of generative chemistry. ACS Med. Chem. Lett. 2020, 11, 1496– 1505,  DOI: 10.1021/acsmedchemlett.0c00088
      28
      The Advent of Generative Chemistry
      Vanhaelen, Quentin; Lin, Yen-Chu; Zhavoronkov, Alex
      ACS Medicinal Chemistry Letters (2020), 11 (8), 1496-1505CODEN: AMCLCT; ISSN:1948-5875. (American Chemical Society)
      A review. Generative adversarial networks (GANs), first published in 2014, are among the most important concepts in modern artificial intelligence (AI). Bridging deep learning and game theory, GANs are used to generate or "imagine" new objects with desired properties. Since 2016, multiple GANs with reinforcement learning (RL) have been successfully applied in pharmacol. for de novo mol. design. Those techniques aim at a more efficient use of the data and a better exploration of the chem. space. We review recent advances for the generation of novel mols. with desired properties with a focus on the applications of GANs, RL, and related techniques. We also discuss the current limitations and challenges in the new growing field of generative chem.
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    29. 29
      Xu, M.; Cheng, J.; Liu, Y.; Huang, W. DeepGAN: Generating Molecule for Drug Discovery Based on Generative Adversarial Network. In 2021 IEEE Symposium on Computers and Communications (ISCC) , 2021; pp 1– 6.
      There is no corresponding record for this reference.
    30. 30
      Guimaraes, G. L.; Sanchez-Lengeling, B.; Outeiral, C.; Farias, P. L. C.; Aspuru-Guzik, A. Objective-reinforced generative adversarial networks (ORGAN) for sequence generation models. arXiv preprint , arXiv:1705.10843, 2017.
      There is no corresponding record for this reference.
    31. 31
      Yu, L.; Zhang, W.; Wang, J.; Yu, Y. SeqGAN: sequence generative adversarial nets with policy gradient. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence , 2017; pp 2852– 2858.
      There is no corresponding record for this reference.
    32. 32
      Prykhodko, O.; Johansson, S. V.; Kotsias, P.-C.; Arús-Pous, J.; Bjerrum, E. J.; Engkvist, O.; Chen, H. A de novo molecular generation method using latent vector based generative adversarial network. J. Cheminf. 2019, 11, 1– 13,  DOI: 10.1186/s13321-019-0397-9
      There is no corresponding record for this reference.
    33. 33
      Kotsias, P.-C.; Arús-Pous, J.; Chen, H.; Engkvist, O.; Tyrchan, C.; Bjerrum, E. J. Direct steering of de novo molecular generation with descriptor conditional recurrent neural networks. Nat. Mach. Intell. 2020, 2, 254– 265,  DOI: 10.1038/s42256-020-0174-5
      There is no corresponding record for this reference.
    34. 34
      De Cao, N.; Kipf, T. MolGAN: An implicit generative model for small molecular graphs. arXiv preprint arXiv:1805.11973 2018,.
      There is no corresponding record for this reference.
    35. 35
      Neukart, F.; Compostella, G.; Seidel, C.; Von Dollen, D.; Yarkoni, S.; Parney, B. Traffic flow optimization using a quantum annealer. Front. ICT 2017, 4, 29,  DOI: 10.3389/fict.2017.00029
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    36. 36
      Harwood, S.; Gambella, C.; Trenev, D.; Simonetto, A.; Bernal Neira, D.; Greenberg, D. Formulating and solving routing problems on quantum computers. IEEE Trans. Quantum Eng. 2021, 2, 1– 17,  DOI: 10.1109/TQE.2021.3049230
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    37. 37
      Orus, R.; Mugel, S.; Lizaso, E. Quantum computing for finance: Overview and prospects. Rev. Phys. 2019, 4, 100028,  DOI: 10.1016/j.revip.2019.100028
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    38. 38
      Liu, G.; Ma, W. A quantum artificial neural network for stock closing price prediction. Inf. Sci. (N.Y.) 2022, 598, 75– 85,  DOI: 10.1016/j.ins.2022.03.064
      There is no corresponding record for this reference.
    39. 39
      Du, Y.; Yang, Y.; Tao, D.; Hsieh, M.-H. Demystify Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification. arXiv preprint , arXiv:2301.01597, 2022.
      There is no corresponding record for this reference.
    40. 40
      Yin, X.-F.; Du, Y.; Fei, Y.-Y.; Zhang, R.; Liu, L.-Z.; Mao, Y.; Liu, T.; Hsieh, M.-H.; Li, L.; Liu, N.-L.; Tao, D.; Chen, Y.-A.; Pan, J.-W. Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver. Phys. Rev. Lett. 2022, 128, 110501,  DOI: 10.1103/PhysRevLett.128.110501
      40
      Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver
      Yin, Xu-Fei; Du, Yuxuan; Fei, Yue-Yang; Zhang, Rui; Liu, Li-Zheng; Mao, Yingqiu; Liu, Tongliang; Hsieh, Min-Hsiu; Li, Li; Liu, Nai-Le; Tao, Dacheng; Chen, Yu-Ao; Pan, Jian-Wei
      Physical Review Letters (2022), 128 (11), 110501CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits, where a two-outcome measurement can be used to query a classical binary result about whether the input state is bipartite entangled or not. In principle, for an N-qubit quantum state, the runtime complexity of our proposal is O(poly(N)T) with T being the no. of iterations. We exptl. implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states. Our work paves the way for using near-term quantum machines to tackle entanglement detection on multipartite entangled quantum systems.
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    41. 41
      Rudolph, M. S.; Toussaint, N. B.; Katabarwa, A.; Johri, S.; Peropadre, B.; Perdomo-Ortiz, A. Generation of high-resolution handwritten digits with an ion-trap quantum computer. Phys. Rev. X 2022, 12, 031010,  DOI: 10.1103/PhysRevX.12.031010
      41
      Generation of High-Resolution Handwritten Digits with an Ion-Trap Quantum Computer
      Rudolph, Manuel S.; Toussaint, Ntwali Bashige; Katabarwa, Amara; Johri, Sonika; Peropadre, Borja; Perdomo-Ortiz, Alejandro
      Physical Review X (2022), 12 (3), 031010CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      Generating high-quality data (e.g., images or video) is one of the most exciting and challenging frontiers in unsupervised machine learning. Utilizing quantum computers in such tasks to potentially enhance conventional machine-learning algorithms has emerged as a promising application but poses big challenges due to the limited no. of qubits and the level of gate noise in available devices. In this work, we provide the first practical and exptl. implementation of a quantum-classical generative algorithm capable of generating high-resoln. images of handwritten digits with state-of-the-art gate-based quantum computers. In our quantum-assisted machine-learning framework, we implement a quantum-circuit-based generative model to learn and sample the prior distribution of a generative adversarial network. We introduce a multibasis technique which leverages the unique possibility of measuring quantum states in different bases, hence enhancing the expressivity of the prior distribution. We train this hybrid algorithm on an ion-trap device based on Yb+171 ion qubits to generate high-quality images and quant. outperform comparable classical generative adversarial networks trained on the popular MNIST dataset for handwritten digits.
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    42. 42
      Aspuru-Guzik, A.; Dutoi, A. D.; Love, P. J.; Head-Gordon, M. Simulated quantum computation of molecular energies. Science 2005, 309, 1704– 1707,  DOI: 10.1126/science.1113479
      42
      Simulated Quantum Computation of Molecular Energies
      Aspuru-Guzik, Alan; Dutoi, Anthony D.; Love, Peter J.; Head-Gordon, Martin
      Science (Washington, DC, United States) (2005), 309 (5741), 1704-1707CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      The calcn. time for the energy of atoms and mols. scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chem. interest using modest nos. of quantum bits. Calcns. of the water and lithium hydride mol. ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estn. algorithm. The recursive algorithm reduces the no. of quantum bits required for the readout register from about 20 to 4. Mappings of the mol. wave function to the quantum bits are described. An adiabatic method for the prepn. of a good approx. ground-state wave function is described and demonstrated for a stretched hydrogen mol. The no. of quantum bits required scales linearly with the no. of basis functions, and the no. of gates required grows polynomially with the no. of quantum bits.
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    43. 43
      Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G.; Goggin, M. E.; Almeida, M. P.; Kassal, I.; Biamonte, J. D.; Mohseni, M.; Powell, B. J.; Barbieri, M.; Aspuru-Guzik, A.; White, A. G. Towards quantum chemistry on a quantum computer. Nat. Chem. 2010, 2, 106– 111,  DOI: 10.1038/nchem.483
      43
      Towards quantum chemistry on a quantum computer
      Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G.; Goggin, M. E.; Almeida, M. P.; Kassal, I.; Biamonte, J. D.; Mohseni, M.; Powell, B. J.; Barbieri, M.; Aspuru-Guzik, A.; White, A. G.
      Nature Chemistry (2010), 2 (2), 106-111CODEN: NCAHBB; ISSN:1755-4330. (Nature Publishing Group)
      Exact first-principles calcns. of mol. properties are currently intractable because their computational cost grows exponentially with both the no. of atoms and basis set size. A soln. is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technol. to calc. properties of the smallest mol. system: the mol. in a minimal basis. We calc. the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chem. problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chem. applications.
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    44. 44
      Peruzzo, A.; McClean, J.; Shadbolt, P.; Yung, M.-H.; Zhou, X.-Q.; Love, P. J.; Aspuru-Guzik, A.; O’brien, J. L. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 2014, 5, 1– 7,  DOI: 10.1038/ncomms5213
      There is no corresponding record for this reference.
    45. 45
      O’Malley, P. J. J.; Babbush, R.; Kivlichan, I. D.; Romero, J.; McClean, J. R.; Barends, R.; Kelly, J.; Roushan, P.; Tranter, A.; Ding, N.; Campbell, B.; Chen, Y.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fowler, A. G.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Coveney, P. V.; Love, P. J.; Neven, H.; Aspuru-Guzik, A.; Martinis, J. M. Scalable quantum simulation of molecular energies. Phys. Rev. X 2016, 6, 031007,  DOI: 10.1103/PhysRevX.6.031007
      45
      Scalable quantum simulation of molecular energies
      O'Malley, P. J. J.; Babbush, R.; Kivlichan, I. D.; Romero, J.; McClean, J. R.; Barends, R.; Kelly, J.; Roushan, P.; Tranter, A.; Ding, N.; Campbell, B.; Chen, Y.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fowler, A. G.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Coveney, P. V.; Love, P. J.; Neven, H.; Aspuru-Guzik, A.; Martinis, J. M.
      Physical Review X (2016), 6 (3), 031007/1-031007/13CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      We report the first electronic structure calcn. performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute the energy surface of mol. hydrogen using two distinct quantum algorithms. First, we exptl. execute the unitary coupled cluster method using the variational quantum eigensolver. Our efficient implementation predicts the correct dissocn. energy to within chem. accuracy of the numerically exact result. Second, we exptl. demonstrate the canonical quantum algorithm for chem., which consists of Trotterization and quantum phase estn. We compare the exptl. performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors. This error tolerance inspires hope that variational quantum simulations of classically intractable mols. may be viable in the near future.
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    46. 46
      Kandala, A.; Mezzacapo, A.; Temme, K.; Takita, M.; Brink, M.; Chow, J. M.; Gambetta, J. M. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 2017, 549, 242– 246,  DOI: 10.1038/nature23879
      46
      Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
      Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan; Takita, Maika; Brink, Markus; Chow, Jerry M.; Gambetta, Jay M.
      Nature (London, United Kingdom) (2017), 549 (7671), 242-246CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
      Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers. Finding exact solns. to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet exptl. implementations have so far been restricted to mols. involving only hydrogen and helium. Here we demonstrate the exptl. optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, detg. the ground-state energy for mols. of increasing size, up to BeH2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepd. trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our expts. and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.
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    47. 47
      Cao, Y.; Romero, J.; Olson, J. P.; Degroote, M.; Johnson, P. D.; Kieferová, M.; Kivlichan, I. D.; Menke, T.; Peropadre, B.; Sawaya, N. P. D.; Sim, S.; Veis, L.; Aspuru-Guzik, A. Quantum Chemistry in the Age of Quantum Computing. Chem. Rev. 2019, 119, 10856– 10915,  DOI: 10.1021/acs.chemrev.8b00803
      47
      Quantum Chemistry in the Age of Quantum Computing
      Cao, Yudong; Romero, Jonathan; Olson, Jonathan P.; Degroote, Matthias; Johnson, Peter D.; Kieferova, Maria; Kivlichan, Ian D.; Menke, Tim; Peropadre, Borja; Sawaya, Nicolas P. D.; Sim, Sukin; Veis, Libor; Aspuru-Guzik, Alan
      Chemical Reviews (Washington, DC, United States) (2019), 119 (19), 10856-10915CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chem. communities over the past century. Although many approxn. methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging complexity landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chem. such as the electronic structure of mols. In the past two decades significant advances have been made in developing algorithms and phys. hardware for quantum computing, heralding a revolution in simulation of quantum systems. This article is an overview of the algorithms and results that are relevant for quantum chem. The intended audience is both quantum chemists who seek to learn more about quantum computing, and quantum computing researchers who would like to explore applications in quantum chem.
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    48. 48
      Quantum, G. A.; Collaborators*†; Arute, F.; Arya, K.; Babbush, R.; Bacon, D.; Bardin, J. C.; Barends, R.; Boixo, S.; Broughton, M. Hartree-Fock on a superconducting qubit quantum computer. Science 2020, 369, 1084– 1089,  DOI: 10.1126/science.abb9811
      There is no corresponding record for this reference.
    49. 49
      Gao, Q.; Nakamura, H.; Gujarati, T. P.; Jones, G. O.; Rice, J. E.; Wood, S. P.; Pistoia, M.; Garcia, J. M.; Yamamoto, N. Computational investigations of the lithium superoxide dimer rearrangement on noisy quantum devices. J. Phys. Chem. A 2021, 125, 1827– 1836,  DOI: 10.1021/acs.jpca.0c09530
      49
      Computational Investigations of the Lithium Superoxide Dimer Rearrangement on Noisy Quantum Devices
      Gao, Qi; Nakamura, Hajime; Gujarati, Tanvi P.; Jones, Gavin O.; Rice, Julia E.; Wood, Stephen P.; Pistoia, Marco; Garcia, Jeannette M.; Yamamoto, Naoki
      Journal of Physical Chemistry A (2021), 125 (9), 1827-1836CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      Quantum chem. studies of biradical systems are challenging due to the required multiconfigurational nature of the wavefunction. In this work, Variational Quantum Eigensolver (VQE) is used to compute the energy profile for the lithium superoxide dimer rearrangement, involving biradical species, on quantum simulators and devices. Considering that current quantum devices can only handle limited no. of qubits, we present guidelines for selecting an appropriate active space to perform computations on chem. systems that require many qubits. We show that with VQE performed with a quantum simulator reproduces results obtained with full-CI (Full CI) for the chosen active space. However, results deviate from exact values by about 39 mHa for calcns. on a quantum device. This deviation can be improved to about 4 mHa using the readout mitigation approach and can be further improved to 2 mHa, approaching chem. accuracy, using the state tomog. technique to purify the calcd. quantum state.
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    50. 50
      Shee, Y.; Yeh, T.-L.; Hsiao, J.-Y.; Yang, A.; Lin, Y.-C.; Hsieh, M.-H. Quantum Simulation of Preferred Tautomeric State Prediction. arXiv preprint , arXiv:2210.02977, 2022.
      There is no corresponding record for this reference.
    51. 51
      Cao, Y.; Romero, J.; Aspuru-Guzik, A. Potential of quantum computing for drug discovery. IBM J. Res. Dev. 2018, 62, 1– 20,  DOI: 10.1147/JRD.2018.2888987
      There is no corresponding record for this reference.
    52. 52
      Li, J.; Topaloglu, R. O.; Ghosh, S. Quantum generative models for small molecule drug discovery. IEEE Trans. Quantum Eng. 2021, 2, 1– 8,  DOI: 10.1109/TQE.2021.3104804
      There is no corresponding record for this reference.
    53. 53
      Bharti, K.; Cervera-Lierta, A.; Kyaw, T. H.; Haug, T.; Alperin-Lea, S.; Anand, A.; Degroote, M.; Heimonen, H.; Kottmann, J. S.; Menke, T.; Mok, W.-K.; Sim, S.; Kwek, L.-C.; Aspuru-Guzik, A. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 2022, 94, 015004,  DOI: 10.1103/RevModPhys.94.015004
      53
      Noisy intermediate-scale quantum algorithms
      Bharti, Kishor; Cervera-Lierta, Alba; Kyaw, Thi Ha; Haug, Tobias; Alperin-Lea, Sumner; Anand, Abhinav; Degroote, Matthias; Heimonen, Hermanni; Kottmann, Jakob S.; Menke, Tim; Mok, Wai-Keong; Sim, Sukin; Kwek, Leong-Chuan; Aspuru-Guzik, Alan
      Reviews of Modern Physics (2022), 94 (1), 015004CODEN: RMPHAT; ISSN:1539-0756. (American Physical Society)
      A review. A universal fault-tolerant quantum computer that can efficiently solve problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the exptl. advancement toward realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e., qubits that are not error cor., and therefore perform imperfect operations within a limited coherence time. In the search for achieving quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chem., and combinatorial optimization. The overarching goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, a thorough summary of NISQ computational paradigms and algorithms is provided. The key structure of these algorithms and their limitations and advantages are discussed. A comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices is addnl. provided.
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    54. 54
      Du, Y.; Hsieh, M.-H.; Liu, T.; Tao, D. Expressive power of parametrized quantum circuits. Phys. Rev. Res. 2020, 2, 033125,  DOI: 10.1103/PhysRevResearch.2.033125
      54
      Expressive power of parametrized quantum circuits
      Du, Yuxuan; Hsieh, Min-Hsiu; Liu, Tongliang; Tao, Dacheng
      Physical Review Research (2020), 2 (3), 033125CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
      Parametrized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum polynomial circuits). In addn., PQCs equipped with ancillary qubits for postselection may possess expressive power stronger than that of those without postselection. We employ them as an application for Bayesian learning, since it is possible to learn prior probabilities rather than assuming they are known. We expect that it will find many more applications in semisupervised learning where prior distributions are normally assumed to be unknown. Lastly, we conduct several numerical expts. using the Rigetti Forest platform to demonstrate the performance of the proposed Bayesian quantum circuit.
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    55. 55
      Du, Y.; Hsieh, M.-H.; Liu, T.; You, S.; Tao, D. Learnability of quantum neural networks. PRX Quantum 2021, 2, 040337,  DOI: 10.1103/PRXQuantum.2.040337
      There is no corresponding record for this reference.
    56. 56
      Du, Y.; Hsieh, M.-H.; Liu, T.; Tao, D.; Liu, N. Quantum noise protects quantum classifiers against adversaries. Phys. Rev. Res. 2021, 3, 023153,  DOI: 10.1103/PhysRevResearch.3.023153
      56
      Quantum noise protects quantum classifiers against adversaries
      Du, Yuxuan; Hsieh, Min-Hsiu; Liu, Tongliang; Tao, Dacheng; Liu, Nana
      Physical Review Research (2021), 3 (2), 023153CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
      Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, esp. in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy. It is then natural to ask: Can we harness the power of quantum noise that is beneficial to quantum computing. An important current direction for quantum computing is its application to machine learning, such as classification problems. One outstanding problem in machine learning for classification is its sensitivity to adversarial examples. These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers. They can also be considered as worst-case perturbations by unknown noise sources. We show that by taking advantage of depolarization noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise. This robustness property is intimately connected with an important security concept called differential privacy, which can be extended to quantum differential privacy. For the protection of quantum data, this quantum protocol can be used against the most general adversaries. Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of the classification model are absent, thus also providing a potential quantum advantage for classical data. This opens the opportunity to explore other ways in which quantum noise can be used in our favor, as well as identifying other ways quantum algorithms can be helpful in a way which is distinct from quantum speedups.
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    57. 57
      Lloyd, S.; Weedbrook, C. Quantum generative adversarial learning. Phys. Rev. Lett. 2018, 121, 040502,  DOI: 10.1103/PhysRevLett.121.040502
      57
      Quantum Generative Adversarial Learning
      Lloyd, Seth; Weedbrook, Christian
      Physical Review Letters (2018), 121 (4), 040502CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Generative adversarial networks represent a powerful tool for classical machine learning: a generator tries to create statistics for data that mimics those of a true data set, while a discriminator tries to discriminate between the true and fake data. The learning process for generator and discriminator can be thought of as an adversarial game, and under reasonable assumptions, the game converges to the point where the generator generates the same statistics as the true data and the discriminator is unable to discriminate between the true and the generated data. This Letter introduces the notion of quantum generative adversarial networks, where the data consist either of quantum states or of classical data, and the generator and discriminator are equipped with quantum information processors. We show that the unique fixed point of the quantum adversarial game also occurs when the generator produces the same statistics as the data. Neither the generator nor the discriminator perform quantum tomog.; linear programing drives them to the optimal. Since quantum systems are intrinsically probabilistic, the proof of the quantum case is different from-and simpler than-the classical case. We show that, when the data consist of samples of measurements made on high-dimensional spaces, quantum adversarial networks may exhibit an exponential advantage over classical adversarial networks.
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    58. 58
      Huang, H.-L.; Du, Y.; Gong, M.; Zhao, Y.; Wu, Y.; Wang, C.; Li, S.; Liang, F.; Lin, J.; Xu, Y.; Yang, R.; Liu, T.; Hsieh, M.-H.; Deng, H.; Rong, H.; Peng, C.-Z.; Lu, C.-Y.; Chen, Y.-A.; Tao, D.; Zhu, X.; Pan, J.-W. Experimental quantum generative adversarial networks for image generation. Phys. Rev. Appl. 2021, 16, 024051,  DOI: 10.1103/PhysRevApplied.16.024051
      58
      Experimental Quantum Generative Adversarial Networks for Image Generation
      Huang, He-Liang; Du, Yuxuan; Gong, Ming; Zhao, Youwei; Wu, Yulin; Wang, Chaoyue; Li, Shaowei; Liang, Futian; Lin, Jin; Xu, Yu; Yang, Rui; Liu, Tongliang; Hsieh, Min-Hsiu; Deng, Hui; Rong, Hao; Peng, Cheng-Zhi; Lu, Chao-Yang; Chen, Yu-Ao; Tao, Dacheng; Zhu, Xiaobo; Pan, Jian-Wei
      Physical Review Applied (2021), 16 (2), 024051CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
      Quantum machine learning is expected to be one of the first practical applications of near-term quantum devices. Pioneer theor. works suggest that quantum generative adversarial networks (GANs) may exhibit a potential exponential advantage over classical GANs, thus attracting widespread attention. However, it remains elusive whether quantum GANs implemented on near-term quantum devices can actually solve real-world learning tasks. Here, we devise a flexible quantum GAN scheme to narrow this knowledge gap. In principle, this scheme has the ability to complete image generation with high-dimensional features and could harness quantum superposition to train multiple examples in parallel. We exptl. achieve the learning and generating of real-world handwritten digit images on a superconducting quantum processor. Moreover, we utilize a gray-scale bar dataset to exhibit competitive performance between quantum GANs and the classical GANs based on multilayer perceptron and convolutional neural network architectures, resp., benchmarked by the Fr´echet distance score. Our work provides guidance for developing advanced quantum generative models on near-term quantum devices and opens up an avenue for exploring quantum advantages in various GAN-related learning tasks.
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    59. 59
      Dallaire-Demers, P.-L.; Killoran, N. Quantum generative adversarial networks. Phys. Rev. A 2018, 98, 012324,  DOI: 10.1103/PhysRevA.98.012324
      59
      Quantum generative adversarial networks
      Dallaire-Demers, Pierre-Luc; Killoran, Nathan
      Physical Review A (2018), 98 (1), 012324CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
      Quantum machine learning is expected to be one of the first potential general-purpose applications of near-term quantum devices. A major recent breakthrough in classical machine learning is the notion of generative adversarial training, where the gradients of a discriminator model are used to train a sep. generative model. In this work and a companion paper, we extend adversarial training to the quantum domain and show how to construct generative adversarial networks using quantum circuits. Furthermore, we also show how to compute gradients-a key element in generative adversarial network training-using another quantum circuit. We give an example of a simple practical circuit ansatz to parametrize quantum machine learning models and perform a simple numerical expt. to demonstrate that quantum generative adversarial networks can be trained successfully.
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      Romero, J.; Aspuru-Guzik, A. Variational quantum generators: Generative adversarial quantum machine learning for continuous distributions. Adv. Quantum Technol. 2021, 4, 2000003,  DOI: 10.1002/qute.202000003
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      Ivanenkov, Y. A.; Polykovskiy, D.; Bezrukov, D.; Zagribelnyy, B.; Aladinskiy, V.; Kamya, P.; Aliper, A.; Ren, F.; Zhavoronkov, A. Chemistry42: An AI-Driven Platform for Molecular Design and Optimization. J. Chem. Inf. Model. 2023, 63, 695– 701,  DOI: 10.1021/acs.jcim.2c01191
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      Chemistry42: An AI-Driven Platform for Molecular Design and Optimization
      Ivanenkov, Yan A.; Polykovskiy, Daniil; Bezrukov, Dmitry; Zagribelnyy, Bogdan; Aladinskiy, Vladimir; Kamya, Petrina; Aliper, Alex; Ren, Feng; Zhavoronkov, Alex
      Journal of Chemical Information and Modeling (2023), 63 (3), 695-701CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Chem.42 is a software platform for de novo small mol. design and optimization that integrates Artificial Intelligence (AI) techniques with computational and medicinal chem. methodologies. Chem.42 efficiently generates novel mol. structures with optimized properties validated in both in vitro and in vivo studies and is available through licensing or collaboration. Chem.42 is the core component of Insilico Medicine's Pharma.ai drug discovery suite. Pharma.ai also includes PandaOmics for target discovery and multiomics data anal., and inClinico-a data-driven multimodal forecast of a clin. trial's probability of success (PoS). In this paper, we demonstrate how the platform can be used to efficiently find novel mol. structures against DDR1 and CDK20.
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      Bergholm, V.; Izaac, J.; Schuld, M.; Gogolin, C.; Ahmed, S.; Ajith, V.; Alam, M. S.; Alonso-Linaje, G.; AkashNarayanan, B.; Asadi, A.; Arrazola, J. M.; Azad, U.; Banning, S.; Blank, C.; Bromley, T. R.; Cordier, B. A.; Ceroni, J.; Delgado, A.; Di Matteo, O.; Dusko, A.; Garg, T.; Guala, D.; Hayes, A.; Hill, R.; Ijaz, A.; Isacsson, T.; Ittah, D.; Jahangiri, S.; Jain, P.; Jiang, E.; Khandelwal, A.; Kottmann, K.; Lang, R. A.; Lee, C.; Loke, T.; Lowe, A.; McKiernan, K.; Meyer, J. J.; Montañez-Barrera, J. A.; Moyard, R.; Niu, Z.; O’Riordan, L. J.; Oud, S.; Panigrahi, A.; Park, C.-Y.; Polatajko, D.; Quesada, N.; Roberts, C.; Sá, N.; Schoch, I.; Shi, B.; Shu, S.; Sim, S.; Singh, A.; Strandberg, I.; Soni, J.; Száva, A.; Thabet, S.; Vargas-Hernández, R. A.; Vincent, T.; Vitucci, N.; Weber, M.; Wierichs, D.; Wiersema, R.; Willmann, M.; Wong, V.; Zhang, S.; Killoran, N. Pennylane: Automatic differentiation of hybrid quantum-classical computations. arXiv preprint , arXiv:1811.04968, 2018.
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      GuacaMol: Benchmarking Models for de Novo Molecular Design
      Brown, Nathan; Fiscato, Marco; Segler, Marwin H. S.; Vaucher, Alain C.
      Journal of Chemical Information and Modeling (2019), 59 (3), 1096-1108CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      De novo design seeks to generate mols. with required property profiles by virtual design-make-test cycles. With the emergence of deep learning and neural generative models in many application areas, models for mol. design based on neural networks appeared recently and show promising results. However, the new models have not been profiled on consistent tasks, and comparative studies to well-established algorithms have only seldom been performed. To standardize the assessment of both classical and neural models for de novo mol. design, we propose an evaluation framework, GuacaMol, based on a suite of standardized benchmarks. The benchmark tasks encompass measuring the fidelity of the models to reproduce the property distribution of the training sets, the ability to generate novel mols., the exploration and exploitation of chem. space, and a variety of single and multiobjective optimization tasks. The benchmarking open-source Python code and a leaderboard can be found on https://benevolent.ai/guacamol.
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      Polykovskiy, D.; Zhebrak, A.; Sanchez-Lengeling, B.; Golovanov, S.; Tatanov, O.; Belyaev, S.; Kurbanov, R.; Artamonov, A.; Aladinskiy, V.; Veselov, M.; Kadurin, A.; Johansson, S.; Chen, H.; Nikolenko, S.; Aspuru-Guzik, A.; Zhavoronkov, A. Molecular sets (MOSES): a benchmarking platform for molecular generation models. Front. Pharmacol. 2020, 11, 565644,  DOI: 10.3389/fphar.2020.565644
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      Molecular sets (MOSES): a benchmarking platform for molecular generation models
      Polykovskiy, Daniil; Zhebrak, Alexander; Sanchez-Lengeling, Benjamin; Golovanov, Sergey; Tatanov, Oktai; Belyaev, Stanislav; Kurbanov, Rauf; Artamonov, Aleksey; Aladinskiy, Vladimir; Veselov, Mark; Kadurin, Artur; Johansson, Simon; Chen, Hongming; Nikolenko, Sergey; Aspuru-Guzik, Alan; Zhavoronkov, Alex
      Frontiers in Pharmacology (2020), 11 (), 565644CODEN: FPRHAU; ISSN:1663-9812. (Frontiers Media S.A.)
      Generative models are becoming a tool of choice for exploring the mol. space. These models learn on a large training dataset and produce novel mol. structures with similar properties. Generated structures can be utilized for virtual screening or training semi-supervized predictive models in the downstream tasks. While there are plenty of generative models, it is unclear how to compare and rank them. In this work, we introduce a benchmarking platform called Mol. Sets (MOSES) to standardize training and comparison of mol. generative models. MOSES provides training and testing datasets, and a set of metrics to evaluate the quality and diversity of generated structures. We have implemented and compared several mol. generation models and suggest to use our results as ref. points for further advancements in generative chem. research. The platform and source code are available at https://github.com/molecularsets/moses.
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      Drug-likeness is a key consideration when selecting compds. during the early stages of drug discovery. However, evaluation of drug-likeness in abs. terms does not reflect adequately the whole spectrum of compd. quality. More worryingly, widely used rules may inadvertently foster undesirable mol. property inflation as they permit the encroachment of rule-compliant compds. towards their boundaries. We propose a measure of drug-likeness based on the concept of desirability called the quant. est. of drug-likeness (QED). The empirical rationale of QED reflects the underlying distribution of mol. properties. QED is intuitive, transparent, straightforward to implement in many practical settings and allows compds. to be ranked by their relative merit. We extended the utility of QED by applying it to the problem of mol. target druggability assessment by prioritizing a large set of published bioactive compds. The measure may also capture the abstr. notion of aesthetics in medicinal chem.
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      We present a new atom type classification system for use in atom-based calcn. of partition coeff. (log P) and molar refractivity (MR) designed in part to address published concerns of previous at. methods. The 68 at. contributions to log P have been detd. by fitting an extensive training set of 9920 mols., with r2 = 0.918 and σ = 0.677. A sep. set of 3412 mols. was used for the detn. of contributions to MR with r2 = 0.997 and σ = 1.43. Both calcns. are shown to have high predictive ability.
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      Landrum, G.; Tosco, P.; Kelley, B.; Sriniker, R.; Gedeck; ; Vianello, R.; Schneider, N.; Kawashima, E.; Dalke, A.; N, D.; Cosgrove, D.; Cole, B.; Swain, M.; Turk, S.; Savelyev, A.; Jones, G.; Vaucher, A.; Wójcikowski, M.; Take, I.; Probst, D.; Ujihara, K.; Scalfani, V. F.; godin, G.; Pahl, A.; Berenger, F.; Varjo, J. L.; Strets, J. P.; Doliath Gavid rdkit/rdkit: 2022_03_1 (Q1 2022) Release. 2022,  DOI: 10.5281/zenodo.6388425 .
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      Ruddigkeit, L.; Van Deursen, R.; Blum, L. C.; Reymond, J.-L. Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17. J. Chem. Inf. Model. 2012, 52, 2864– 2875,  DOI: 10.1021/ci300415d
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      Enumeration of 166 Billion Organic Small Molecules in the Chemical Universe Database GDB-17
      Ruddigkeit, Lars; van Deursen, Ruud; Blum, Lorenz C.; Reymond, Jean-Louis
      Journal of Chemical Information and Modeling (2012), 52 (11), 2864-2875CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Drug mols. consist of a few tens of atoms connected by covalent bonds. How many such mols. are possible in total and what is their structure. This question is of pressing interest in medicinal chem. to help solve the problems of drug potency, selectivity, and toxicity and reduce attrition rates by pointing to new mol. series. To better define the unknown chem. space, we have enumerated 166.4 billion mols. of up to 17 atoms of C, N, O, S, and halogens forming the chem. universe database GDB-17, covering a size range contg. many drugs and typical for lead compds. GDB-17 contains millions of isomers of known drugs, including analogs with high shape similarity to the parent drug. Compared to known mols. in PubChem, GDB-17 mols. are much richer in nonarom. heterocycles, quaternary centers, and stereoisomers, densely populate the third dimension in shape space, and represent many more scaffold types.
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      Schuld, M.; Petruccione, F. Supervised Learning with Quantum Computers, Vol. 17; Springer, 2018.
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      Schuld, M.; Bocharov, A.; Svore, K. M.; Wiebe, N. Circuit-centric quantum classifiers. Phys. Rev. A 2020, 101, 032308,  DOI: 10.1103/PhysRevA.101.032308
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      Circuit-centric quantum classifiers
      Schuld, Maria; Bocharov, Alex; Svore, Krysta M.; Wiebe, Nathan
      Physical Review A (2020), 101 (3), 032308CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
      Variational quantum circuits are becoming tools of choice in quantum optimization and machine learning. In this paper we investigate a class of variational circuits for the purposes of supervised machine learning. We propose a circuit architecture suitable for predicting class labels of quantumly encoded data via measurements of certain observables. We observe that the required depth of a trainable classification circuit is related to the no. of representative principal components of the data distribution. Quantum circuit architectures used in our design are validated by numerical simulation, which shows significant model size redn. compared to classical predictive models. Circuit-based models demonstrate good resilience to noise, which makes then robust and error tolerant.
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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.3c00562.

    • Different complexities of generators in MolGAN; different input noise dimensions of the generator in MolGAN-HR; different parametrized layers of QuMolGAN-HR; all the combinations of the classical/quantum noise/generator/discriminator and their corresponding model name; different numbers of qubits in the quantum circuit of QuMolGAN-HR; the details of MolGAN-CC models with the varied size of discriminators; example molecules from the quantum generator; integration of proposed hybrid generative models with Insilico Medicine Chemistry42 (62) platform; example molecules of QM9 (PDF)


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