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.
In the field of drug discovery, efficiently designing molecular structures with optimal chemical properties and synthetic accessibility is a complex and important research area.
Typical approaches such as iterating through the design and experiment cycle can only search a small region in a vast chemical space, where the number of synthesizable molecules of size acceptable for drugs is estimated to be over 10 60 1 . Machine learning and deep learning-based drug design can efficiently explore a wider region in such a huge chemical space. Actually, by applying recent achievements in deep learning and deep generative models, various deep generative models have been reported for molecules with desired chemical properties 2,3 . Despite these efforts, two challenges with compounds generated from existing generative models remain: 1) the low frequency of “drug-like” molecules that satisfy the activity to the target proteins and have acceptable chemical properties and synthetic accessibility; and 2) a trade-off between the character of the compounds and the diversity in the chemical structure 4 . One cause of these problems is the lack of data, resulting in low generalization due to overfitting. Currently, the number of compounds that can be synthesized is ~10 10 5 , whereas the expected size of the chemical space is 10 60 (as previously mentioned)-thus, the number of synthesizable compounds represents only a very small proportion of the entire chemical search space, and is insufficient for use as training data.
Quantum machine learning (QML) (also referred to as quantum artificial intelligence (QAI)) is a growing area of research that combines quantum computing and machine learning.
QML investigates how quantum resources such as superposition, entanglement, and tunneling can accelerate or enhance classical learning models. Most early work has focused on the gatebased paradigm, where data and model parameters are encoded into quantum circuits composed of unitary transformations and projective measurements. Algorithms such as quantum support vector machines, kernel estimators, and quantum neural networks are implemented through parameterized quantum circuits, optimized using hybrid quantumclassical feedback loops 6 . However, in many common scenarios, training parameterized quantum circuits has been shown to be unlikely to be able to scale due to trainability issues known as barren plateaus 7 ; it may also be possible for classical computing to efficiently simulate such quantum circuits 8 .
An alternative and more physically motivated framework arises in quantum annealing 9,10 , which provides an analog realization of optimization and sampling tasks central to machine learning. In quantum annealing, learning problems are mapped onto an Ising Hamiltonian and the system searches for the low-energy configurations. Sampling from these configurations can be guided by training the parameters of the Ising Hamiltonian to learn a “binary” data distribution or a “binary” latent representation of an autoencoder. Quantum annealers, such as D-Wave’s Advantage2™ quantum computer, implement these dynamics in hardware, enabling large-scale exploration of complex energy landscapes for machine learning applications [11][12][13] . Recent experiments have demonstrated that quantum annealing achieves a scaling advantage in approaching low-energy configurations 14,15 , while the resulting sampling distributions cannot be efficiently reproduced by any known classical simulation 15 . Therefore, it is important to explore ways to harness this intrinsic sampling power for quantum-enhanced generative modeling in areas such as drug discovery and materials design.
In this report, our approach started from Variational Autoencoder (VAE)-based generative models for generation and inference of chemical compounds. VAE sets the approximated posterior distribution of the latent variables and optimizes the evidence lower bound (ELBO) instead of the true log-likelihood, which is generally intractable. By the amortized inference and the reparameterization framework 16,17 , VAE can efficiently train its objective function, which is also referred to as the loss function with the reconstruction loss and regularization terms included, and is widely used for the generative model. TransVAE 3 also involves the VAE that generates character sequences of molecules via a combination of Transformer-based Encoder/Decoder and continuous-valued latent space. More recently, VAE with discrete latent variables, Discrete VAE (DVAE) 18 , in which the generative process is driven by a Boltzmann Machine (BM), was adopted for the generation of chemical compounds 19 .
DVAE incorporates discrete latent variables with a discrete prior, making it a more suitable alternative for modeling data with categorical structures such as molecular descriptors tokenized by employing a particular transformation scheme. In addition, DVAE is suitable for combining a VAE architecture with qu
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