Quantum Generative Models for Small Molecule Drug Discovery
QQuantum Generative Models for Small MoleculeDrug Discovery
Junde Li
Pennsylvania State University [email protected]
Rasit Topaloglu
Swaroop Ghosh
Pennsylvania State University [email protected]
Abstract —Existing drug discovery pipelines take 5-10 yearsand cost billions of dollars. Computational approaches aim tosample from regions of the whole molecular and solid-state com-pounds called chemical space which could be on the order of .Deep generative models can model the underlying probabilitydistribution of both the physical structures and property of drugsand relate them nonlinearly. By exploiting patterns in massivedatasets, these models can distill salient features that characterizethe molecules. Generative Adversarial Networks (GANs) discoverdrug candidates by generating molecular structures that obeychemical and physical properties and show affinity towardsbinding with the receptor for a target disease. However, classicalGANs cannot explore certain regions of the chemical space andsuffer from curse-of-dimensionality. A full quantum GAN mayrequire more than 90 qubits even to generate QM9-like smallmolecules. We propose a qubit-efficient quantum GAN with ahybrid generator (QGAN-HG) to learn richer representation ofmolecules via searching exponentially large chemical space withfew qubits more efficiently than classical GAN. The QGAN-HG model is composed of a hybrid quantum generator thatsupports various number of qubits and quantum circuit layers,and, a classical discriminator. QGAN-HG with only 14.93%retained parameters can learn molecular distribution as effi-ciently as classical counterpart. The QGAN-HG variation withpatched circuits considerably accelerates our standard QGAN-HG training process and avoids potential gradient vanishingissue of deep neural networks. Code is available on GitHubhttps://github.com/jundeli/quantum-gan. I. I
NTRODUCTION
Drug development pipeline consists of stages of targetdiscovery, molecular design, preclinical studies, and clinicaltrials, which makes the process of creating a marketabledrug expensive and time consuming [1]. The majority ofnew drugs approved by US Food and Drug Administration issmall-molecule drugs whose structural and functional diversitymake their matching with biological binding sites possible[2]. Searching new drugs can be considered as navigatingin the chemical space, which is the ensemble of all organicmolecules, and navigation in unknown chemical space fallswithin the field of de novo drug design [3].Machine learning techniques have been explored in alldevelopment stages, especially molecular design with desirableproperties [1], [4], [5]. Generative models such as, variationalautoencoders (VAEs) [6], generative adversarial networks(GANs) [7] and recurrent neural networks (RNNs) are specif-ically adopted for learning latent representations of moleculesand generating large amount of drug candidates for fur-ther high-throughput screening. Deep generative models havebeen used for various representation types of molecules such as, string-based, graph-based and shape/structure-based [8]–[12] representations. Generative learning with graph-structuredmolecules is invariant to the orderings of atoms [10], [13]and automates the navigation to a chemical region abundantin desired molecules. However, classical generative modelscannot generate all possible distributions indicating that itcannot explore certain regions of the chemical space. This isprimarily due to exponential choices to gradually add a newmolecule in the existing drug fragment. Note, drug discoverycan be explained using lock and key model where the receptor(a protein binding site associated with a disease) is consideredas a lock and the drug is a key (Fig. 1(a)). If the shape andpose of the drug is right, it can plug into the binding sitecuring the disease.Quantum computing can offer unique advantages over clas-sical computing in many areas such as, chemistry simula-tion, machine learning, and optimization [14]–[16]. QuantumGAN is one of the main applications of near-term quantumcomputers due to its strong expressive power in learningdata distributions even with much less parameters comparedto classical GANs [17]. Quantum GANs can offer severalopportunities e.g., (i) quantum speedup in the runtime makingit possible to learn richer representation of molecules viadeeper models due to the amplitude amplification property;(ii) ability to search exponentially large chemical space withfew qubits and sample from distributions that may be difficultto model classically.Quantum GAN is still at its nascent stage due to qubitconstraints on noisy quantum computers. Huang et al. [18]proposed a quantum patch GAN mechanism to efficientlyuse limited qubits for generating hand-written digit images,however, the method only suits two digits of 0 and 1. QuGAN[17] aims to learn MNIST data set, but the original 784-dimension images were reduced to only 2 dimensions.
To thebest of our knowledge, no existing quantum GAN mechanismscan essentially solve real-world complicated learning tasks .Drug molecules can be represented as graphs where thenodes and edges correspond to atoms and bonds, respectively.Given the task complexity of learning molecule distribution,full quantum GAN can hardly encode all training data in aquantum way. Take the small molecule dataset QM9 [20] forexample. The total number of qubits required for reconstruct-ing synthetic molecules is (cid:0) (cid:1) log 5 + 9 log 5 > where 5 isthe number of bond types and atom types contained in QM9.No commercially available quantum computers support over a r X i v : . [ c s . ET ] J a n ..... F a k e F a k e R e a l R e a l DrugPropertiesDrugProperties
Fréchet distance
Fréchet distance0/10/1(d)Atom LayerAtom LayerBond LayerBond Layer NH2N NCN NH2N NCN + (c)(a) ...... P a r a m e t e r i z e d Q u a n t u m C i r c u i t P a r a m e t e r i z e d Q u a n t u m C i r c u i t ... ... P a r a m e t e r i z e d Q u a n t u m C i r c u i t ... ... ... P a r a m e t e r i z e d Q u a n t u m C i r c u i t ... ... Docking engineBinding site
Drug fragments Docking engineBinding site
Drug fragments (b)
Fig. 1. (a) Only generated molecules that have high affinity towards the receptor binding sites are considered as valid; (b) quantum stage (which is aparameterized quantum circuit with last-layer N measuring the expectation values) and classical stage (neural network with last-layer out-feature dimensionof 512 [10]) separated by blue dotted line; (c) application of atom layer and bond layer for generating synthetic molecular graphs (one example syntheticmolecule is given); (d) a batch of real molecules from training dataset (QM9 in this case) and a batch of synthetic molecules generated from (c) are fedinto classical discriminator for real/synthetic prediction and FD score calculation, and drug properties for synthetic molecules are evaluated using RDKitpackage [19]. The prediction losses from discriminator are back-forwarded to two neural networks as well as quantum circuit for updating all parameterssimultaneously in each training epoch.
90 qubits at present. The proposed quantum GAN model canovercome the qubit constraint while still exploiting the benefitsof quantum computing.We propose a qubit-efficient quantum GAN mechanismwith hybrid generator and classical discriminator for efficientlylearning molecule distributions based on classical MolGAN[10]. Since the proposed quantum GAN requires less qubits,simulation is still a viable option for training unlike full quan-tum GAN with large number qubits that cannot be simulatedusing classical computers. We also examine the patched circuitidea [18] by comparing to the original single large generatorcircuit implementation using metric of Fr´echet distance anddrug property scores. Fig. 1 shows the overall workflow of ourqubit-efficient hybrid quantum GAN model for drug discovery.
This work aims to discover a library of novel and validmolecules that can be screened by the docking engine in thenext step (Fig. 1(a)).
Novelty/contributions:
To the best of our knowledge, thisis the first work on drug discovery using quantum machinelearning . We, (1) propose a novel quantum GAN mechanismwith hybrid generator to qubit-efficiently tackle any real-world learning tasks solvable on classical GANs; (2) generatepotentially better drug molecular graphs in terms of Fr´echetdistance (FD) score and drug property scores, and achievehigh training efficiency by reducing generator architecturecomplexity; (3) examine the performance of patched quantumGAN for drug discovery task and comparison is made withQGAN-HG with a single quantum circuit; (4) validate thecapability of generating small drug molecules on real IBMquantum computers by running inference stage of QGAN-HGmodel (not for training stage due to long waiting time on IBMQ machines per iteration).II. B
ACKGROUND
A. Computational Drug Discovery
Generative models such as, GAN [7] have been exploredfor discovery of drug molecules with desired properties bylearning drug molecule distribution based on given chemicaldataset and sample synthetic molecules from the chemicalspace. GAN consists of two networks, namely generator (G) and discriminator (D), competing with each other. Thegenerator uses noise as input to generate synthetic data samplewhereas the discriminator flags if given sample is real orfake with a binary classifier. Generator G ( z ; θ g ) maps randominput noise z to synthetic chemical data space p g , whilediscriminator D ( x ; θ d ) outputs a single scalar indicating theprobability that x come from real data rather than p g . D istrained to maximize the probability to assign correct label andG is trained to minimize the difference between real and fake log(1 − D ( G ( z ))) . The two-player minimax game is trainedbased on the following value function: min θ g max θ d V ( D, G ) = E x ∼ p data ( x ) [log D ( x )]+ E z ∼ p z ( z ) [log(1 − D ( G ( z )))] Chemical compounds can be represented as graphs withnodes and edges designating various atoms and their bonds,respectively. For example, Fig. 2(a-b) shows a molecule and itsgraph representation where atom types of N and O are encodedas 2 and 3 in atom vector, and bond types of single anddouble are encoded as 1 and 2 in bond matrix. If the generatedstructure is chemically stable and exhibits high affinity towardsthe receptor binding sites then it can be treated as a validdrug molecule. The generator and discriminator are trainedusing example drugs/molecules until the synthetic chemicaldistribution is close to real chemical space. The quality ofGAN outcome are measured by Fr´echet distance and RDKit(for chemical properties) [19].
B. Quantum Machine Learning
Quantum systems have atypical patterns that classical com-puters cannot produce efficiently [14]. Machine learning tasksare sometimes hard to train on classical computers due tolarge-scale and high-dimensional data set. Quantum neuralnetwork (QNN) can represent given dataset, either quantum orclassical, and be trained using a series of parameter dependentunitary transformations. QNN architecture is dependent onqubit count, quantum circuit layer, and quantum gates appliedbecause the architecture is essentially a variational quantum = A = NO 𝑅 𝑧 θ = 𝑒 −𝑖θ2
00 𝑒 𝑖θ2 𝑅 𝑦 θ = 𝑐𝑜𝑠 θ2 − 𝑠𝑖𝑛 θ2𝑠𝑖𝑛 θ2 𝑐𝑜𝑠 θ2 CNOT (a) (b) (c)
Fig. 2. (a-b) A sample molecular graph from QM9 denoted by its corre-sponding atom vector A and bond matrix B; (c) all quantum gates used inthis study. circuit. Thus, below quantum computing concepts are helpfulin understanding quantum neural network.
Quantum Circuit:
Quantum circuits consist of gates thatmodulate the state of the qubits to perform computation. Gatepulses induce a varied amount of rotation along the axes in theBloch sphere. Quantum gates could be applied on 1 qubit (e.g.,rotation gates R y and R z ) or 2 qubits (e.g., CNOT gate), asshown in Fig. 2(c). Finally, measurement is applied for gettingthe expectation value after certain number of shots. Quantum Noise:
Noisy quantum computers suffer fromnoise sources such as, T1 relaxation time, T2 dephasingtime, gate errors and readout error. These are also calledqubit quality metrics. Crosstalk, qubit-to-qubit variation andtemporal variations in qubit quality also exist. Fortunately,reasonable quantum noise level is not detrimental for QNN,rather it can even be beneficial because systematic noise ishelpful for improving generalization performance of neuralnetworks. Instead of mitigating such noises, we rather explorethe effect of quantum noise by running the inference forQGAN-HG on a real IBM quantum computer.III. Q
UANTUM G ENERATIVE A DVERSARIAL N ETWORKS
A. Quantum GAN Flavors
Quantum GAN has a few flavors of the generator and dis-criminator implementations depending on their execution en-vironments, either on quantum computers, classical machinesor quantum simulators. The flavor with quantum discriminatoris not applicable here due to limited number of qubits on near-term quantum computers. Real data shown in Fig. 1(d) has toengage the state preparation stage, usually through amplitudeencoding, for encoding classical data in a quantum state, andthis stage takes N log( M ) qubits where N is the trainingset size and M is feature dimension [18], [21]. The flavorwith a pure quantum generator is not directly applicable eitherconsidering the complicated task of drug discovery. As notedin Section I, more than 90 qubits are needed to discover QM9-like molecules (not suitable for near-term quantum computers).Thus we propose a new quantum GAN with hybrid generatorand classical discriminator to exploit the quantum benefits. B. Quantum GAN with Hybrid Generator
Quantum GAN with hybrid generator (QGAN-HG) is com-posed of a parameterized quantum circuit to get a featurevector of qubit size dimension, and a classical deep neuralnetwork to output an atom vector and a bond matrix for the
Initialization
Layers
Parameterized Layers (repeat for L times)
Feature
Vector |0 ⟩ |0 ⟩ |0 ⟩ |0 ⟩ ... ... ... ... R Y (z ) Z( θ )Z( θ n+2 ) Z( θ N+1 ) R Y ( θ ) R Y ( θ ) R Y ( θ )R Y ( θ n ) R Y (z ) R Y (z ) R Y (z ) R Z (z ) R Z (z ) R Z (z )R Z (z ) Fig. 3. Parameterized quantum circuit to obtain feature vector of N dimen-sions. The circuit is composed of initialization layers, repeatable parameter-ized layers and measurement layer. Two CNOT gates for each ZZ interactionfor creating entanglement are not shown here. graph representation of drug molecules. Another patched quan-tum GAN with hybrid generator (P-QGAN-HG) is consideredas the variation of QGAN-HG where the quantum circuit isformed by concatenating few quantum sub-circuits.
QGAN-HG Quantum Circuit:
In this variant, a quantumlayer is added for exploiting the strong expressive powerof variational quantum circuits which perform low-rank ma-trix computations in O ( poly (log( M ))) time for exponentialspeedup [18], [22]. The variational quantum circuit (Fig.3) consists of 3 stages, namely initialization, parameterized(repeatable for L layers with L (2 N − parameter count) andmeasurement stages. Two parameters z and z are uniformlysampled from [ − π, π ] , which essentially substitute the randomGaussian noise input for classical GANs. After applying theinitialization layers, the input state in mathematical form | z (cid:105) = ( ⊗ Ni =1 R Z ( z ) R Y ( z ) | (cid:105) ) ⊗ N is prepared. Let us denotethe parameterized layers repeated for L times as unitary matrix U ( θ ) . The final quantum state is of the form | Ψ( z ) (cid:105) = U ( θ ) | z (cid:105) . A series of measurement operators are applied toobtain the expectation value for each qubit and further formthe feature vector to be fed to classical neural network. QGAN-HG Neural Network:
This classical stage of hybridgenerator is a standard neural network with input layer receiv-ing the feature vector of expectation values. The final layerconsists of the separate atom and bond layers for creating atomvectors and bond matrices, respectively. Like MolGAN [10],a categorical re-parameterization step with Gumbel-Softmax[23], which supports gradient calculation in the backward pass,is taken for getting discrete fake molecular graphs. Note that,85.07% and 98.03% of generator parameters are respectivelycropped by reducing major linear layers from classical GAN[10] so as to demonstrate the strong expressive power ofquantum circuits. Due to the necessity of reconstructing QM9-like molecules (with structure of X ∈ R X for atoms and A ∈ R X X for bonds), neural network architecture canhardly be further reduced. Patched QGAN-HG:
The patched quantum GAN withhybrid generator consists of the same two ingredients asabove. However, the parameterized quantum circuit consistsof multiple quantum sub-circuits. Theoretically, P-QGAN-HG has its pros and cons relative to QGAN-HG with anintegral quantum circuit. P-QGAN-HG requires less quantum
10 20 30 40 50
Samples F r é c he t D i s t an c e FD A+B 128FD A+B 512
Samples F r é c he t D i s t an c e FD B 128FD B 512
Samples M o l e c u l e P r ope r t i e s QEDlogPSA (a) (b) (c)
Fig. 4. Metrics of Fr´echet distance and molecule properties for real data points: (a) Fr´echet distances calculated based on both Atom and Bond (A+B) withbatches of 128 molecules and 512 molecules; (b) Fr´echet distances calculated based on only Bond (B) for batch sizes of 128 and 512; (c) three major drugproperties evaluated on sample batches of 128 molecules from (a). Note that these 50 samples are independently sampled from QM9. resources because multiple sub-circuits can be executed se-quentially or in parallel. Another benefit is that each circuitcan be simulated more efficiently, which speeds up the learningprocess accordingly. However, one of the obvious drawbacksis reduced expressive power since quantum state dimensionis reduced from N to N/ (say two circuits with half size)in Hilbert space. The performance of patched QGAN-HG iscompared with QGAN-HG in the following section. Discriminator and Optimizer:
The discriminator is keptthe same as MolGAN [10] as its parameter size is at par withthe hybrid generator. However, the reward network is discardedsince reward value is too minuscule to noticeably contribute totraining the model. Generated molecules are evaluated usingRDKit together with Fr´echet distance based metric. Quantumgate parameters and weights in neural network are updatedsimultaneously using a single optimizer, while discriminatoruses a separate one for being updated alternatively.IV. E
XPERIMENTAL S ETUP
A. Dataset and Metrics
Dataset:
All the experiments are conducted with quantummachine learning benchmarking QM9 [20] dataset whichcontains 133,885 molecules with up to 9 heavy atoms of typesof carbon, nitrogen, oxygen, and fluorine.
Fr´echet Distance:
Learning results of the proposed GANsare evaluated with Fr´echet distance metric which measures thesimilarity between real and generated molecule distributions.Generated molecule distribution is approximately created bygenerating a batch of molecules, and real one is approximatelyformed by randomly sampling the same number of moleculesfrom QM9 dataset. Each sample batch of molecules is concate-nated and considered as a multi-dimensional point in the dis-tribution, then Fr´echet distance is calculated using 50 of thesepoints (sampled for 50 batches from both distributions). Fig. 4shows Fr´echet distances calculated from two batch sizes of 128and 512 molecules and independently sampled for 50 times.FD A+B (see Fig. 4(a)) denotes the similarity calculated basedon both atom and bond matrices; while FD B (see Fig. 4(b))only on bond matrices. FD A+B includes more random noisesfrom molecule atoms and is projected to severely disturbthe similarity between real molecule batches. Interestingly,FD A+B correlates well with the distance calculated without atoms. This is a strong evidence of the inherent connectionbetween atoms and bonds. The means (12.3342, 12.6387) andvariations (0.7057, 0.7849) between FD calculated for 128 and512 batch sizes are close. Thus, all following experiments areevaluated with FD A+B metric and 128 batch size.
Drug Properties:
Molecule properties are the metrics fordrug quality evaluation during inference stage. Three primaryproperties include, (i) quantitative estimate of druglikeness(QED) which measures the likelihood of compound being adrug; (ii) log octanol-water partition coefficient (logP) whichmeasures the solubility of a compound; and (iii) and syntheticaccessibility (SA) which quantifies the ease of a compoundbeing synthesized in pharmaceutical factory. Together withother properties, they are measured using RDKit.
B. Implementation Details
The quantum circuits can be executed either on a simulatoror real quantum machine. The simulator supports customizedsetting of noise levels and sources (noiseless environment isset in this paper), while real quantum devices have differentnoise characteristics across different machines.
Training:
We pivot on the classical MolGAN [10] toimplement our QGAN-HG and P-QGAN-HG algorithms. Asmentioned in Section III, some linear layers and rewardnetwork are removed in our experiments for evaluating theexpressive power of quantum circuit and using drug propertymetrics fairly. Our QGAN variations are trained with a mini-batch of 128 molecules using Adam optimizer on a single RTX2080 Ti GPU for classical part and PennyLane platform [24]with default qubit plugin for the quantum stage. As explainedin Section I, real quantum machine is not utilized duringtraining stage due to long waiting time on IBM Q machines.The learning rate is initially set to 0.0001 for both generatorand discriminator and starts decaying uniformly at a factorof / after 3000 epochs. Total training epoch is set with5000, and early stopping based on Fr´echet distance is appliedif model collapse happens. Inference:
Only hybrid generator is involved during infer-ence stage. Since QGAN is well trained, the quantum circuitin the generator is executed on both PennyLane simulator andreal quantum device of IBM Q16 Melbourne for comparison.Drug quality for generated molecules are evaluated by proper-ties such as, QED, logP, and SA, among others, all of which
Training Epochs F r é c he t D i s t an c e QGAN MRMolGAN MRMolGAN
Training Epochs F r é c he t D i s t an c e QGAN HRMolGAN HR
Training Epochs F r é c he t D i s t an c e QGAN L2QGAN Q10
Training Epochs F r é c he t D i s t an c e P2-QGANP4-QGAN M G A N M G A N M R M G A N H R
Q G A N M R Q G A N H R
Q G A N L2 Q G A N Q P - Q G A N P - Q G A N T r a i n i ng E po c h s ( K ) M G A N M G A N M R M G A N H R
Q G A N M R Q G A N H R
Q G A N L2 Q G A N Q P - Q G A N P - Q G A N T r a i n i ng T i m e ( s ) (a) (b) (c)(d) (e) (f) Fig. 5. Training comparison among GAN flavors: (a) Fr´echet distances for MolGAN, moderately reduced (14.93%) MolGAN and QGAN-HG; (b) Fr´echetdistances for highly reduced (1.97%) MolGAN and QGAN-HG; (c) learning curves for highly reduced QGAN-HG with quantum circuit level L = 2 and N = 10 , respectively; (d) learning curves for patched QGAN-HG with two sub-circuits (4 qubits for each) and four sub-circuits (2 qubits for each); (e)training epochs with lowest Fr´echet distances for all GAN flavors; (f) training times elapsed (early stopping at epochs from (e)) for all GAN flavors. are normalized to be within [0 , . Finally, GAN variations arecompared by taking 1000 generated molecules.V. E VALUATION R ESULTS
A. QGAN-HG Results
Fig. 3 shows QGAN-HG performance may rely on bothqubit count N and repeatable layer count L . Higher qubitcount and layer count presumably correspond to stronger ex-pressive power of hybrid generator. To demonstrate expressivepower, we reduce the neural network parameter count to twolevels, namely, 14.93% ( MR -moderately reduced) and 1.97%( HR -highly reduced) of generator parameters of original Mol-GAN. Fig. 5(a-b) show the training performance comparisonbetween MolGAN and QGAN-HG for moderately and highlyreduced architectures, respectively. One can observe fromFig. 5(a) that all mechanisms can reach a reasonably goodtraining point (see Fig. 4 for benchmark) within 5000 epochs,however, moderately reduced MolGAN takes around 4000iterations while original MolGAN and QGAN-HG take only2500 iterations or so. Also note that, MolGAN and QGAN-HGboth reach a slightly lower Fr´echet distance than the reducedclassical counterpart. As shown in Fig. 5(b), MolGAN withhighly reduced architecture can hardly be learned though aslight downward trend is observed. The weak learning abilityof MolGAN-HR is attributed to mainly two reasons: (1) thefeatures of QM9 drug molecules cannot be well representedusing a light-weight neural network; (2) parameter count ofgenerator is not at par with that of discriminator. Intriguingly,a sharp downward learning curve for QGAN-HG is stillobserved. It is worth mentioning that only 15 gate parametersare involved in the quantum circuit. These are clear evidencesof strong expressive power of variational quantum circuits.Model collapsing occur for GAN variations if Fr´echetdistances (approximate indicator of learning quality) start increasing after certain training point. We adopt early stoppingtechnique (the lowest reached point of Fr´echet distance) tosomewhat prevent the training instability issue in GANs. Tomeasure the effects of circuit layer and qubit count, we alsoimplement QGAN-HG with L = 2 and N = 10 separately.However, the enhanced QGAN-HG variations with more cir-cuit layer and qubits (see Fig. 5(c, e)) do not help acceleratelearning process much relative to QGAN-HG in Fig. 5(b). B. P-QGAN-HG Results
The patched QGAN-HG mechanism is developed on thebasis of [18], however, P-QGAN-HG we proposed here usesall qubits for creating feature vector and has no specific qubitsfor non-linear mapping because of the following classicalneural network. We demonstrate the expressive power of twopatched QGAN-HG variations, i.e. P2-QGAN with two sub-circuits (each has 4 qubits and 7 gate parameters) and P4-QGAN with four sub-circuits (each has 2 qubits and 3 gateparameters). Surprisingly, the learning quality of these patchedQGANs are comparable to QGAN with an integral circuit, asshown in Fig. 5(a, d), though patched QGANs have even lessgate parameters. Further, the simulation time (see Fig. 5(f))for patched quantum circuits are significantly reduced becauseof smaller qubit count and early convergence. Therefore, weconsider patched QGAN-HG with multiple sub-circuits is analternative to classical GAN since GAN training issues suchas instability and vanishing gradients can be mitigated byshortening neural network depth.
C. Drug Properties
The training of GAN variations is evaluated by Fr´echetdistance, whereas the quality of drug molecules generated fromGANs is specifically evaluated using a series of moleculeproperty metrics, three of which are visualized in Fig. 4(c).
ABLE ID
RUG PROPERTIES OF
GENERATED MOLECULES FROM ALL
GAN
VARIATIONS IN THIS PAPER . B
EST RESULTS ARE SHOWN IN BOLD . S
IGN ’-’
INDICATES THE CORRESPONDING METRIC FOR SAMPLED MOLECULES ARE NOT SUCCESSFULLY EVALUATED BY
RDK IT .Method Druglikeliness Solubility Synthesizability Diversity Valid Unique NovelMolGAN ∗ [10] 0.50 MolGAN MR 0.47 0.60 0.14
MolGAN HR - - -
QGAN-HG MR (proposed)
QGAN-HG HR (proposed) - - -
QGAN-HG HR L2 (proposed) - - -
QGAN-HG HR Q10 (proposed) 0.49 0.43 0.15
P2-QGAN-HG MR (proposed) 0.49 0.62 0.11
P4-QGAN-HG MR (proposed) 0.49 0.51 0.13
QGAN-HG MR (on IBM quantum computer) 0.48 0.50
MolGAN ∗ refers to MolGAN [10] trained in the present study. The drug property evaluation is performed by a specificinference stage. All GAN variations pick a point with lowestFr´echet distance within 5000 epochs for inference. We alsorun the inference stage for QGAN-HG on IBM Q quantummachines as well. Drug properties are calculated using 1000sampled molecules. Table I displays the drug property resultswhich are generally consistent with Fr´echet distance results.Note that diversity and novel scores for all models are high,whereas synthetic accessibility is low relative to benchmarkshown in Fig. 4(c). QGAN-HG results executed on simulatorand real quantum computer are consistent except the lattershows higher unique and systhesizability scores.VI. C
ONCLUSION
We propose a novel quantum GAN with a hybrid genera-tor for discovery of new drug molecules. Our hybrid GANwith patched quantum circuits concatenates feature vectorsfrom different patches. Results show that classical GAN with85.07% reduced parameters cannot properly learn moleculedistribution, however our QGAN-HG with only 15 extraquantum gate parameters can learn molecular task at par withoriginal GAN. The proposed QGAN-HG with 98.03% reducedparameters is significantly efficient than the highly reducedclassical counterpart. The patched quantum GAN achievescomparable learning accuracy in terms of drug properties witheven only 12 extra quantum gate parameters, and considerablyaccelerates the quantum GAN with an integral quantum circuit.The proposed patched quantum GAN model can be alternativeto classical GAN due to less training time and avoidance ofpossible gradient vanishing problem in deep neural networks.R
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