Latent Style-based Quantum Wasserstein GAN for Drug Design

Julien Baglio; Yacine Haddad; Richard Polifka

quant-phMar 23, 2026

Latent Style-based Quantum Wasserstein GAN for Drug Design

Authors: Julien Baglio, Yacine Haddad, Richard Polifka

Organizations: Center for Quantum Computing and Quantum Coherence (QC2), Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland · QuantumBasel, Schorenweg 44b, CH-4144 Arlesheim, Switzerland · Laboratory for High Energy Physics (LHEP), Physics Institute, Faculty of Sciences, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland · Open Quantum Institute and Quantum Technology Initiative, CERN, Esplanade des Particules 1, CH-1211 Geneva 23, Switzerland

Abstract

The development of new drugs is a tedious, time-consuming, and expensive process, for which the average costs are estimated to be up to around $2.5 billion. The first step in this long process is the design of the new drug, for which de novo drug design, assisted by artificial intelligence, has blossomed in recent years and revolutionized the field. In particular, generative artificial intelligence has delivered promising results in drug discovery and development, reducing costs and the time to solution. However, classical generative models, such as generative adversarial networks (GANs), are difficult to train due to barren plateaus and prone to mode collapse. Quantum computing may be an avenue to overcome these issues and provide models with fewer parameters, thereby enhancing the generalizability of GANs. We propose a new style-based quantum GAN (QGAN) architecture for drug design that implements noise encoding at every rotational gate of the circuit and a gradient penalty in the loss function to mitigate mode collapse. Our pipeline employs a variational autoencoder to represent the molecular structure in a latent space, which is then used as input to our QGAN. Our baseline model runs on up to 15 qubits to validate our architecture on quantum simulators, and a 156-qubit IBM Heron quantum computer in the five-qubit setup is used for inference to investigate the effects of using real quantum hardware on the analysis. We benchmark our results against classical models as provided by the MOSES benchmark suite.

Figures & tables

Figure 1: Schematic representation of the quantum-augmented drug-design pipeline. The model comprises a pre-trained VAE on the MOSES dataset using SMILES input (in purple), that embeds the original molecules into a low-dimensional latent space, and a quantum GAN with a quantum generator (in red) and a classical discriminator (in blue). The features extracted by the VAE from the input dataset are used for the training of the GAN. The final generated SMILES molecules are reconstructed by inversely transforming the features generated by the quantum generator using the pre-trained decoder of the VAE, and finally validated using RDKit.

Figure 2: Styled simple circuit with five qubits and one layer.

Figure 3: Styled basic entangled layer (BEL) circuit with five qubits and one layer. In addition there is a final set of one-qubit

R_{Y}

gates on each qubit to rotate all qubits in the computational basis before performing the final measurement operation.

Metrics	Nominal VAE	Tuned VAE
Learning rate (lr)	$3\times 10^{-4}$	Scheduled $10^{-3}\rightarrow 10^{-5}$
Encoder $n_{l}$	1	1
Encoder $D_{h}$	256	512
Decoder $n_{l}$	3	4
Decoder $D_{h}$	512	512
Decoder dropout	0	0.75

Table 1: VAE hyperparameter settings comparison between nominal (MOSES default) and tuned settings.

Metrics	Train set	Nominal VAE	Tuned VAE
IntDiv	0.898	0.896	0.896
$\mathcal{W}(\text{LogP})$	0.091	0.087	0.079
$\mathcal{W}(\text{SA})$	0.268	0.275	0.251
$\mathcal{W}(\text{QED})$	0.027	0.025	0.022
$\mathcal{W}(\text{Weight})$	42.8	43.9	41.8
$N_{params}$	–	4,271,250	6,472,082

Table 2: Metrics derived from the training set and sets generated by the nominal and tuned VAE. Internal diversity is computed as the mean over the respective samples, whereas the remaining four metrics are the average Wasserstein distances between the sample in question and the test sample for the corresponding metric.

Panel of Figure 4 — Figure 4: Distributions of metrics derived from the input train set and the generated sets using the nominal and tuned VAE decoder.

Figure 5: Comparison of the loss functions for the nominal (left) and tuned (right) GANs. Each model was run with five different seeds, the shaded band denotes a

\pm 1\sigma

deviation.

Metrics	Train set	Tuned VAE	Nominal GAN	Tuned GAN
$\epsilon_{d}$	0.982	0.605 $\pm$ 0.017	0.510 $\pm$ 0.007	0.481 $\pm$ 0.030
$\epsilon_{v}$	1.000	0.868 $\pm$ 0.006	0.911 $\pm$ 0.006	0.917 $\pm$ 0.012
$\epsilon_{u}$	1.000	0.993 $\pm$ 0.001	0.986 $\pm$ 0.002	0.986 $\pm$ 0.003
Novelty	0.000	0.461 $\pm$ 0.026	0.501 $\pm$ 0.015	0.536 $\pm$ 0.015
Filters	0.734	0.728 $\pm$ 0.002	0.723 $\pm$ 0.003	0.721 $\pm$ 0.011
IntDiv	0.898	0.896 $\pm$ 0.000	0.902 $\pm$ 0.002	0.898 $\pm$ 0.004

Table 3: Metrics results for the VAE and classical GANs. All GANs use the tuned VAE for the latent space representation. Unlike the other cases, the nominal GAN uses the nominal GAN hyperparameter settings as discussed in the text. The quoted standard deviation comes from running each scenario five times with different seeds for the initialization of the trainable parameters.

Panel of Figure 6 — Figure 6: Comparison of the metrics for the models used in the analysis. For the VAE, the tuned version is used, for the GAN, not only the tuned VAE is used but also the GAN is tuned itself. Each model was run with five different seeds, the shaded band is defined as $\pm 1\sigma$ deviation.

Figure 7: Comparison of the loss functions for the nominal (left) and tuned (right) quantum GANs with the BEL circuit. Each model was run with five different seeds, the shaded band is defined as

\pm 1\sigma

deviation.

Metrics	Tuned GAN	Simple QGAN	BEL QGAN
$N_{params}$	705,162	20	110
$\epsilon_{d}$	$0.481\pm 0.031$	$0.529\pm 0.003$	$0.523\pm 0.003$
$\epsilon_{v}$	$0.917\pm 0.012$	$0.831\pm 0.002$	$0.875\pm 0.003$
$\epsilon_{u}$	$0.986\pm 0.003$	$0.994\pm 0.000$	$0.993\pm 0.001$
Novelty	$0.536\pm 0.015$	$0.572\pm 0.003$	$0.548\pm 0.003$
IntDiv	$0.898\pm 0.004$	$0.882\pm 0.000$	$0.883\pm 0.000$

Table 4: Comparison of the performance of the two types of quantum GANs with respect to the classical GAN. All models use tuned VAE and GAN training parameters. The quantum circuit use five qubits, two layers and dual readout to produce a latent vector of dimension 10.

Panel of Figure 8 — Figure 8: Comparison of the metrics for the two quantum circuits and the classical GAN. All models use tuned VAE and GAN training parameters. The quantum circuit uses five qubits, two layers and dual readout to produce a latent vector of dimension 10. Each model was run with five different seeds and the shaded band is defined as $\pm 1\sigma$ deviation.

Figure 9: Distribution of latent vectors for the train, test, classical GAN and BEL QGAN samples.

Latent Dimension	GAN			Simple QGAN		BEL QGAN
( $N_{params}$ )		Readout	$n_{qb}$	$n_{l}=2$	$n_{l}=4$	$n_{l}=2$	$n_{l}=4$	$n_{l}=6$
( $N_{params}$ )		Readout	$n_{qb}$	( $n_{par}$ )	( $n_{par}$ )	( $n_{par}$ )	( $n_{par}$ )	( $n_{par}$ )
10	Reference	Dual	5	-1.00	-1.01	-0.26	-0.27
10		Dual	5	(20)	(40)	(110)	(210)
(705,162)		Single	10	-0.84	-0.83	-0.10	-0.08	-0.11
(705,162)		Single	10	(40)	(80)	(220)	(420)	(620)

Table 5: Average

\langle Z_{0}\rangle

comparison of different scenarios between classical GANs and QGANs using different setup for the QGANs. The numbers in parenthesis in the first column are the number of trainable parameters and reflect the model capacity (i.e. complexity).

Metrics	Classical GAN	QGAN (noiseless)	QGAN (ibm_kingston)
$\epsilon_{d}$	0.689	0.892	0.892
$\epsilon_{v}$	0.947	0.934	0.955
$\epsilon_{u}$	0.990	1.000	1.000
Novelty	0.310	0.338	0.336
IntDiv	0.915	0.881	0.890
Filters	0.719	0.706	0.729

Table 6: Metrics comparison calculated with 2,500 generated molecules, between classical GAN, the style QGAN on noiseless simulator, and the style QGAN inference on ibm_kingston. The quantum generator uses

n_{qb}=5

, a number of layers

n_{l}=2

, and dual readout.

Panel of Figure 10 — Figure 10: Distributions of LogP, SA, and QED metrics for the generation of 2,500 molecule using a classical GAN, the style QGAN ran noiseless simulator, and the style QGAN ran on ibm_kingston. The quantum generator uses $n_{qb}=5$ , a number of layers $n_{l}=2$ , and dual readout.

Figure 11: Random selection of the 2,500 generated molecules sampled on ibm_kingston, passing the RDKit filters and all new compared to both the training and test dataset. The purple cluster contains molecules with LogP values compatible with injectable drugs; the pink cluster contains molecules with LogP values ideal for oral ingestion; the green cluster contains all other molecules with LogP not in the previous categories and still viable drug candidates with $|\text{LogP}|<5$ .

Appendix figures & tables29 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 12 — Figure 12: Comparison of metrics distributions between the input train and test sets.

Metrics	Train set	Test set
IntDiv	0.898	0.889
$\mathcal{W}(\text{LogP})$	0.091	–
$\mathcal{W}(\text{SA})$	0.268	–
$\mathcal{W}(\text{QED})$	0.027	–
$\mathcal{W}(\text{Weight})$	42.8	–

Appendix

Table 7: Comparison of metrics between the input train and test sets.

Figure 13: VAE loss function as a function of number of training epochs for the nominal VAE.

$N_{ep}$	100	250	800	1,000
GPU runtime	9m 10s	17m 24s	48m 49s	52m 35s
IntDiv	0.892	0.919	0.896	0.896
$\mathcal{W}(\text{LogP})$	0.190	0.030	0.048	0.048
$\mathcal{W}(\text{SA})$	0.258	0.2646	0.2796	0.2751
$\mathcal{W}(\text{QED})$	0.084	0.090	0.096	0.097
$\mathcal{W}(\text{Weight})$	67.6	51.2	43.8	43.9

Appendix

Table 8: VAE metrics comparison for the four

N_{ep}

points. The Wasserstein distance is measured between the test and generated samples. While the internal diversity is maximized, all other metrics are minimized. We also report the GPU runtime for comparison.

Panel of Figure 14 — Figure 14: Metrics distributions for models trained with different number of epochs. Stabilization of the results starts with 800 epochs.

$N_{generated}$	30,000	300,000	1,000,000
GPU runtime	52m	1h 37m	2h 12m
Sampling runtime	10m	55m	1h 30m
$\epsilon_{d}$	0.479	0.168	0.120
$\epsilon_{v}$	0.889	0.704	0.609
$\epsilon_{u}$	0.996	0.982	0.977
$N_{Canonical}$	12,725	34,763	71,118

Appendix

Table 9: Metrics comparison for the nominal VAE training for three different sizes of sets of generated molecules. We also report runtime on the GPU.

lr max	$3\times 10^{-4}$	$1\times 10^{-4}$	$1\times 10^{-2}$	$5\times 10^{-5}$	$5\times 10^{-3}$	$1\times 10^{-3}$
lr min	$3\times 10^{-4}$	$1\times 10^{-6}$	$1\times 10^{-4}$	$5\times 10^{-5}$	$5\times 10^{-3}$	$1\times 10^{-5}$
$\epsilon_{d}$	0.479	0.805	0.938	0.842	0.936	0.417
$\epsilon_{v}$	0.889	0.660	0.018	0.626	0.041	0.957
$\epsilon_{u}$	0.996	0.986	0.956	0.985	0.940	0.997
Novelty	0.237	0.702	0.925	0.768	0.856	0.119
IntDiv	0.896	0.893	0.887	0.891	0.929	0.898

Appendix

Table 10: Comparisons of the results of VAE learning rate tuning, the first column corresponds to the nominal scenario. Individual scenarios are defined by the learning rate minima/maxima at the top of the Table.

Panel of Figure 15 — Figure 15: Metrics distributions for models trained with different learning rates. Clear breakdown for the 0.01-0.0001 and 0.005 scenarios is visible.

$n_{l}$	1	2	1	1
$D_{h}$	256	256	128	512
Dropout	0.0	0.5	0.0	0.0
$\epsilon_{d}$	0.479	0.548	0.475	0.5321
$\epsilon_{v}$	0.889	0.838	0.888	0.8552
$\epsilon_{u}$	0.996	0.994	0.995	0.9933
Novelty	0.237	0.349	0.238	0.327

Appendix

Table 11: Comparisons of the results of VAE encoder parameter tuning, the first column corresponds to the nominal scenario. The scenario variation is highlighted at the top of the table. The dropout is active only for a scenario with more than one encoder layer, in such case value of 0.5 was used.

Panel of Figure 16 — Figure 16: Metrics distributions for models trained with different encoder settings. Results are very similar between the different scenarios.

$n_{l}$	3	2	4	3	3	3	3
$D_{h}$	512	512	512	256	1024	512	512
Dropout	0.0	0.0	0.0	0.0	0.0	0.25	0.75
$\epsilon_{d}$	0.479	0.590	0.487	0.718	0.416	0.480	0.556
$\epsilon_{v}$	0.889	0.818	0.869	0.718	0.944	0.911	0.875
$\epsilon_{v}$	0.996	0.990	0.996	0.988	0.997	0.996	0.994
Novelty	0.237	0.429	0.240	0.573	0.126	0.248	0.378

Appendix

Table 12: Comparisons of the results of VAE decoder parameter tuning, the first column corresponds to the nominal scenario. The scenario variation is highlighted at the top of the table. The default decoder dropout is zero regardless the number of layers.

Panel of Figure 17 — Figure 17: Metrics distributions for models trained with different decoder settings. Results are very similar for the different scenarios.

Figure 18: Distributions of 10 latent vectors used as inputs of the VAE decoder.

Panel of Figure 19 — Figure 19: Metric distribution obtained from SMILES sets which were generated by the VAE decoder from various latent vector distributions. Additional scenario – VAE(gen) – corresponds to a set which is generated by the standard MOSES sampling procedure. The distributions are normalized to unit area.

Panel of Figure 20 — Figure 20: Correlations between individual latent vectors for the training set, test set, classical GAN training output, and BEL QGAN training output, all for a latent dimension of 10.

Latent dimension	QGAN			Table	Figures
Latent dimension	$n_{qb}$	$n_{l}$	Readout	Table	Figures
10	5	2	Dual	14	8
10	5	4	Dual	15	21
10	10	2	Single	16	22
10	10	4, 6	Single	17	23
20	10	2	Dual	18	24

Appendix

Table 13: Summary of the different scenarios and links to the corresponding individual tables and figures.

Metrics	Classical tuned	Styled simple QGAN	$Z_{0}$	styled BEL QGAN	$Z_{0}$
$N_{params}$	705,162	20		110
$\epsilon_{d}$	$0.481\pm 0.031$	$0.529\pm 0.003$	$+1.56$	$0.523\pm 0.003$	$+1.36$
$\epsilon_{v}$	$0.917\pm 0.012$	$0.831\pm 0.002$	$-7.21$	$0.875\pm 0.003$	$-3.43$
$\epsilon_{u}$	$0.986\pm 0.003$	$0.994\pm 0.000$	$+3.50$	$0.993\pm 0.001$	$+2.90$
Novelty	$0.536\pm 0.015$	$0.572\pm 0.003$	$+2.40$	$0.548\pm 0.003$	$+0.82$
IntDiv	$0.898\pm 0.004$	$0.882\pm 0.000$	$-4.60$	$0.883\pm 0.000$	$-4.21$

Appendix

Table 14: Tuned classical GAN vs QGANs with

n_{qb}=5

n_{l}=2

, and dual readout.

Metrics	Classical tuned	Styled simple QGAN	$Z_{0}$	Styled BEL QGAN	$Z_{0}$
$N_{params}$	705,162	40		210
$\epsilon_{d}$	$0.481\pm 0.031$	$0.526\pm 0.003$	$+1.46$	$0.522\pm 0.004$	$+1.32$
$\epsilon_{v}$	$0.917\pm 0.012$	$0.830\pm 0.002$	$-7.24$	$0.876\pm 0.004$	$-3.36$
$\epsilon_{u}$	$0.986\pm 0.003$	$0.994\pm 0.000$	$+3.42$	$0.993\pm 0.001$	$+2.80$
Novelty	$0.536\pm 0.015$	$0.577\pm 0.003$	$+2.72$	$0.548\pm 0.004$	$+0.76$
IntDiv	$0.898\pm 0.004$	$0.882\pm 0.000$	$-4.66$	$0.883\pm 0.000$	$-4.21$

Appendix

Table 15: Tuned classical GAN vs QGANs with

n_{qb}=5

n_{l}=4

, and dual readout.

Panel of Figure 21 — Figure 21: Metrics distributions for classical and quantum models. All GANs are trained with a latent dimension of 10. The quantum GANs use $n_{qb}=5$ , $n_{l}=4$ , and dual readout.

Metrics	Classical tuned	Styled simple QGAN	$Z_{0}$	Styled BEL QGAN	$Z_{0}$
$N_{params}$	716,692	40		220
$\epsilon_{d}$	$0.481\pm 0.031$	$0.514\pm 0.004$	$+1.06$	$0.514\pm 0.002$	$+1.06$
$\epsilon_{v}$	$0.917\pm 0.012$	$0.833\pm 0.003$	$-6.99$	$0.887\pm 0.003$	$-2.45$
$\epsilon_{u}$	$0.986\pm 0.003$	$0.994\pm 0.000$	$+3.27$	$0.992\pm 0.001$	$+2.45$
Novelty	$0.536\pm 0.015$	$0.586\pm 0.003$	$+3.34$	$0.548\pm 0.002$	$+0.82$
IntDiv	$0.898\pm 0.004$	$0.882\pm 0.000$	$-4.68$	$0.884\pm 0.000$	$-3.99$

Appendix

Table 16: Tuned classical GAN vs QGANs with

n_{qb}=10

n_{l}=2

, and single readout.

Panel of Figure 22 — Figure 22: Metrics distributions for classical and quantum models. All GANs are trained with a latent dimension of 10. The quantum GANs use $n_{qb}=10$ , $n_{l}=2$ , and single readout.

Metrics	Classical tuned	Styled simple QGAN	$Z_{0}$	Styled BEL QGAN	$Z_{0}$	styled BEL	$Z_{0}$
$n_{l}$	-	4		4		6
$N_{params}$	705,162	80		420		620
$\epsilon_{d}$	$0.481\pm 0.031$	$0.515\pm 0.005$	$+1.08$	$0.516\pm 0.005$	$+1.13$	$0.515\pm 0.003$	$+1.10$
$\epsilon_{v}$	$0.917\pm 0.012$	$0.833\pm 0.002$	$-6.95$	$0.887\pm 0.003$	$-2.42$	$0.888\pm 0.002$	$-2.41$
$\epsilon_{u}$	$0.986\pm 0.003$	$0.994\pm 0.000$	$+3.26$	$0.992\pm 0.001$	$+2.48$	$0.992\pm 0.001$	$+2.62$
Novelty	$0.536\pm 0.015$	$0.586\pm 0.002$	$+3.37$	$0.549\pm 0.002$	$+0.87$	$0.550\pm 0.001$	$+0.93$

Appendix

Table 17: Tuned classical GAN vs QGANs with

n_{qb}=10

n_{l}=4,6

, and single readout.

Panel of Figure 23 — Figure 23: Metrics distributions for classical and quantum models. All GANs are trained with a latent dimension of 10. The quantum GANs use $n_{qb}=10$ , $n_{l}=4$ and 6, and single readout.

Metrics	Classical tuned	Styled simple QGAN	$Z_{0}$	Styled BEL QGAN	$Z_{0}$
Latent dimension	20	20		20
$N_{params}$	716,692	40		220
$\epsilon_{d}$	0.526 $\pm$ 0.022	0.507 $\pm$ 0.003	$-0.85$	0.519 $\pm$ 0.005	$-0.32$
$\epsilon_{v}$	0.901 $\pm$ 0.008	0.911 $\pm$ 0.004	$+1.23$	0.910 $\pm$ 0.002	$+1.22$
$\epsilon_{u}$	0.990 $\pm$ 0.002	0.991 $\pm$ 0.001	$+0.25$	0.991 $\pm$ 0.001	$+0.05$
Novelty	0.488 $\pm$ 0.018	0.484 $\pm$ 0.001	$-0.22$	0.484 $\pm$ 0.002	$-0.25$

Appendix

Table 18: Quantum GANs with latent dimension of 20,

n_{qb}=10

n_{l}=2

, and dual readout.

Panel of Figure 24 — Figure 24: Metrics distributions for classical and quantum models. All GANs are trained with a latent dimension of 20. The quantum GANs use $n_{qb}=10$ , $n_{l}=2$ , and dual readout.

Metrics	Classical tuned	Styled simple QGAN	$Z_{0}$	Styled BEL QGAN	$Z_{0}$
Latent dimension	30	30		30
$N_{params}$	728,222	60		330
$\epsilon_{d}$	0.500 $\pm$ 0.066	0.496 $\pm$ 0.003	$-0.06$	0.504 $\pm$ 0.002	$+0.07$
$\epsilon_{v}$	0.884 $\pm$ 0.032	0.895 $\pm$ 0.002	$+0.32$	0.903 $\pm$ 0.003	$+0.57$
$\epsilon_{u}$	0.990 $\pm$ 0.004	0.992 $\pm$ 0.001	$+0.42$	0.991 $\pm$ 0.001	$+0.39$
Novelty	0.504 $\pm$ 0.018	0.476 $\pm$ 0.003	$-1.55$	0.471 $\pm$ 0.003	$-1.81$

Appendix

Table 19: Quantum GANs with a latent dimension of 30,

n_{qb}=15

n_{l}=2

, and dual readout.

Panel of Figure 25 — Figure 25: Metrics distributions for classical and quantum models. All GANs are trained with a latent dimension of 30. The quantum GANs use $n_{qb}=15$ , $n_{l}=2$ , and dual readout.

Latent Dimension	10	20	$Z_{0}$	30	$Z_{0}$
$N_{params}$	$705,162$	$716,692$		$728,222$
$\epsilon_{d}$	$0.481\pm 0.031$	$0.526\pm 0.022$	$+1.19$	$0.500\pm 0.066$	$+0.25$
$\epsilon_{v}$	$0.917\pm 0.012$	$0.901\pm 0.008$	$-1.16$	$0.884\pm 0.032$	$-0.96$
$\epsilon_{u}$	$0.986\pm 0.003$	$0.990\pm 0.002$	$+1.59$	$0.990\pm 0.004$	$+0.84$
Novelty	$0.536\pm 0.015$	$0.488\pm 0.018$	$-2.04$	$0.504\pm 0.018$	$-1.39$
IntDiv	$0.898\pm 0.004$	$0.893\pm 0.002$	$-1.19$	$0.896\pm 0.003$	$-0.43$

Appendix

Table 20: Classical GAN comparison of different latent dimensions.

Panel of Figure 26 — Figure 26: Metrics distributions for classical models trained with different latent dimensions.

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Deep generative modeling to stochastically design small molecules is an emerging technology for accelerating drug discovery and development. However, one major issue in molecular generative models is their lower frequency of drug-like compounds. To resolve this problem, we developed a novel framework for optimization of deep generative models integrated with a D-Wave quantum annealing computer, where our Neural Hash Function (NHF) presented herein is used both as the regularization and binarization schemes simultaneously, of which the latter is for transformation between continuous and discrete signals of the classical and quantum neural networks, respectively, in the error evaluation (i.e., objective) function. The compounds generated via the quantum-annealing generative models exhibited higher quality in both validity and drug-likeness than those generated via the fully-classical models, and was further indicated to exceed even the training data in terms of drug-likeness features, without any restraints and conditions to deliberately induce such an optimization. These results indicated an advantage of quantum annealing to aim at a stochastic generator integrated with our novel neural network architectures, for the extended performance of feature space sampling and extraction of characteristic features in drug design.

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