Navigating the vast chemical space of molecular structures to design novel drug molecules with desired target properties remains a central challenge in drug discovery. Recent advances in generative models offer promising solutions. This work presents a novel quantum circuit Born machine (QCBM)-enabled Generative Adversarial Network (GAN), called QCA-MolGAN, for generating drug-like molecules. The QCBM serves as a learnable prior distribution, which is associatively trained to define a latent space aligning with high-level features captured by the GANs discriminator. Additionally, we integrate a novel multi-agent reinforcement learning network to guide molecular generation with desired targeted properties, optimising key metrics such as quantitative estimate of drug-likeness (QED), octanol-water partition coefficient (LogP) and synthetic accessibility (SA) scores in conjunction with one another. Experimental results demonstrate that our approach enhances the property alignment of generated molecules with the multi-agent reinforcement learning agents effectively balancing chemical properties.

The discovery of small molecules with therapeutic potential is a long-standing challenge in chemistry and biology. Researchers have increasingly leveraged novel computational techniques to streamline the drug development process to increase hit rates and reduce the costs associated with bringing a drug to market. To this end, we introduce a quantum-classical generative model that seamlessly integrates the computational power of quantum algorithms trained on a 16-qubit IBM quantum computer with the established reliability of classical methods for designing small molecules. Our hybrid generative model was applied to designing new KRAS inhibitors, a crucial target in cancer therapy. We synthesized 15 promising molecules during our investigation and subjected them to experimental testing to assess their ability to engage with the target. Notably, among these candidates, two molecules, ISM061-018-2 and ISM061-22, each featuring unique scaffolds, stood out by demonstrating effective engagement with KRAS. ISM061-018-2 was identified as a broad-spectrum KRAS inhibitor, exhibiting a binding affinity to KRAS-G12D at $1.4 \mu M$. Concurrently, ISM061-22 exhibited specific mutant selectivity, displaying heightened activity against KRAS G12R and Q61H mutants. To our knowledge, this work shows for the first time the use of a quantum-generative model to yield experimentally confirmed biological hits, showcasing the practical potential of quantum-assisted drug discovery to produce viable therapeutics. Moreover, our findings reveal that the efficacy of distribution learning correlates with the number of qubits utilized, underlining the scalability potential of quantum computing resources. Overall, we anticipate our results to be a stepping stone towards developing more advanced quantum generative models in drug discovery.

We present hierarchical learning, a novel variational architecture for efficient training of large-scale variational quantum circuits. We test and benchmark our technique for distribution loading with quantum circuit born machines (QCBMs). With QCBMs, probability distributions are loaded into the squared amplitudes of computational basis vectors represented by bitstrings. Our key insight is to take advantage of the fact that the most significant (qu)bits have a greater effect on the final distribution and can be learned first. One can think of it as a generalization of layerwise learning, where some parameters of the variational circuit are learned first to prevent the phenomena of barren plateaus. We briefly review adjoint methods for computing the gradient, in particular for loss functions that are not expectation values of observables. We first compare the role of connectivity in the variational ansatz for the task of loading a Gaussian distribution on nine qubits, finding that 2D connectivity greatly outperforms qubits arranged on a line. Based on our observations, we then implement this strategy on large-scale numerical experiments with GPUs, training a QCBM to reproduce a 3-dimensional multivariate Gaussian distribution on 27 qubits up to $\sim4\%$ total variation distance. Though barren plateau arguments do not strictly apply here due to the objective function not being tied to an observable, this is to our knowledge the first practical demonstration of variational learning on large numbers of qubits. We also demonstrate hierarchical learning as a resource-efficient way to load distributions for existing quantum hardware (IBM's 7 and 27 qubit devices) in tandem with Fire Opal optimizations.

Quantum machine learning (QML) is a cross-disciplinary subject made up of two of the most exciting research areas: quantum computing and classical machine learning (ML), with ML and artificial intelligence (AI) being projected as the first fields that will be impacted by the rise of quantum machines. Quantum computers are being used today in drug discovery, material & molecular modelling and finance. In this work, we discuss some upcoming active new research areas in application of quantum machine learning (QML) in finance. We discuss certain QML models that has become areas of active interest in the financial world for various applications. We use real world financial dataset and compare models such as qGAN (quantum generative adversarial networks) and QCBM (quantum circuit Born machine) among others, using simulated environments. For the qGAN, we define quantum circuits for discriminators and generators and show promises of future quantum advantage via QML in finance.

In recent proposals of quantum circuit models for generative tasks, the discussion about their performance has been limited to their ability to reproduce a known target distribution. For example, expressive model families such as Quantum Circuit Born Machines (QCBMs) have been almost entirely evaluated on their capability to learn a given target distribution with high accuracy. While this aspect may be ideal for some tasks, it limits the scope of a generative model's assessment to its ability to memorize data rather than generalize. As a result, there has been little understanding of a model's generalization performance and the relation between such capability and the resource requirements, e.g., the circuit depth and the amount of training data. In this work, we leverage upon a recently proposed generalization evaluation framework to begin addressing this knowledge gap. We first investigate the QCBM's learning process of a cardinality-constrained distribution and see an increase in generalization performance while increasing the circuit depth. In the 12-qubit example presented here, we observe that with as few as 30% of the valid data in the training set, the QCBM exhibits the best generalization performance toward generating unseen and valid data. Lastly, we assess the QCBM's ability to generalize not only to valid samples, but to high-quality bitstrings distributed according to an adequately re-weighted distribution. We see that the QCBM is able to effectively learn the reweighted dataset and generate unseen samples with higher quality than those in the training set. To the best of our knowledge, this is the first work in the literature that presents the QCBM's generalization performance as an integral evaluation metric for quantum generative models, and demonstrates the QCBM's ability to generalize to high-quality, desired novel samples.

Quantum generative models, in providing inherently efficient sampling strategies, show promise for achieving a near-term advantage on quantum hardware. Nonetheless, important questions remain regarding their scalability. In this work, we investigate the barriers to the trainability of quantum generative models posed by barren plateaus and exponential loss concentration. We explore the interplay between explicit and implicit models and losses, and show that using implicit generative models (such as quantum circuit-based models) with explicit losses (such as the KL divergence) leads to a new flavour of barren plateau. In contrast, the Maximum Mean Discrepancy (MMD), which is a popular example of an implicit loss, can be viewed as the expectation value of an observable that is either low-bodied and trainable, or global and untrainable depending on the choice of kernel. However, in parallel, we highlight that the low-bodied losses required for trainability cannot in general distinguish high-order correlations, leading to a fundamental tension between exponential concentration and the emergence of spurious minima. We further propose a new local quantum fidelity-type loss which, by leveraging quantum circuits to estimate the quality of the encoded distribution, is both faithful and enjoys trainability guarantees. Finally, we compare the performance of different loss functions for modelling real-world data from the High-Energy-Physics domain and confirm the trends predicted by our theoretical results.

Generative modeling has seen a rising interest in both classical and quantum machine learning, and it represents a promising candidate to obtain a practical quantum advantage in the near term. In this study, we build over a proposed framework for evaluating the generalization performance of generative models, and we establish the first quantitative comparative race towards practical quantum advantage (PQA) between classical and quantum generative models, namely Quantum Circuit Born Machines (QCBMs), Transformers (TFs), Recurrent Neural Networks (RNNs), Variational Autoencoders (VAEs), and Wasserstein Generative Adversarial Networks (WGANs). After defining four types of PQAs scenarios, we focus on what we refer to as potential PQA, aiming to compare quantum models with the best-known classical algorithms for the task at hand. We let the models race on a well-defined and application-relevant competition setting, where we illustrate and demonstrate our framework on 20 variables (qubits) generative modeling task. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models. Such a feature is highly desirable in a wide range of real-world applications where the available data is scarce.

Due to the linearity of quantum mechanics, it remains a challenge to design quantum generative machine learning models that embed non-linear activations into the evolution of the statevector. However, some of the most successful classical generative models, such as those based on neural networks, involve highly non-linear dynamics for quality training. In this paper, we explore the effect of these dynamics in quantum generative modeling by introducing a model that adds non-linear activations via a neural network structure onto the standard Born Machine framework - the Quantum Neuron Born Machine (QNBM). To achieve this, we utilize a previously introduced Quantum Neuron subroutine, which is a repeat-until-success circuit with mid-circuit measurements and classical control. After introducing the QNBM, we investigate how its performance depends on network size, by training a 3-layer QNBM with 4 output neurons and various input and hidden layer sizes. We then compare our non-linear QNBM to the linear Quantum Circuit Born Machine (QCBM). We allocate similar time and memory resources to each model, such that the only major difference is the qubit overhead required by the QNBM. With gradient-based training, we show that while both models can easily learn a trivial uniform probability distribution, on a more challenging class of distributions, the QNBM achieves an almost 3x smaller error rate than a QCBM with a similar number of tunable parameters. We therefore provide evidence that suggests that non-linearity is a useful resource in quantum generative models, and we put forth the QNBM as a new model with good generative performance and potential for quantum advantage.

The quantum circuit Born machine (QCBM) is a quantum physics inspired implicit generative model naturally suitable for learning binary images, with a potential advantage of modeling discrete distributions that are hard to simulate classically. As data samples are generated quantum-mechanically, QCBMs encompass a unique optimization landscape. However, pioneering works on QCBMs do not consider the practical scenario where only small batch sizes are allowed during training. QCBMs trained with a statistical two-sample test objective in the image space require large amounts of projective measurements to approximate the model distribution well, unpractical for large-scale quantum systems due to the exponential scaling of the probability space. QCBMs trained adversarially against a deep neural network discriminator are proof-of-concept models that face mode collapse. In this work we investigate practical learning of QCBMs. We use the information-theoretic \textit{Maximal Coding Rate Reduction} (MCR$^2$) metric as a second moment matching tool and study its effect on mode collapse in QCBMs. We compute the sampling based gradient of MCR$^2$ with respect to quantum circuit parameters with or without an explicit feature mapping. We experimentally show that matching up to the second moment alone is not sufficient for training the quantum generator, but when combined with the class probability estimation loss, MCR$^2$ is able to resist mode collapse. In addition, we show that adversarially trained neural network kernel for infinite moment matching is also effective against mode collapse. On the Bars and Stripes dataset, our proposed techniques alleviate mode collapse to a larger degree than previous QCBM training schemes, moving one step closer towards practicality and scalability.

Generative modeling is a promising task for near-term quantum devices, which can use the stochastic nature of quantum measurements as a random source. So called Born machines are purely quantum models and promise to generate probability distributions in a quantum way, inaccessible to classical computers. This paper presents an application of Born machines to Monte Carlo simulations and extends their reach to multivariate and conditional distributions. Models are run on (noisy) simulators and IBM Quantum superconducting quantum hardware. More specifically, Born machines are used to generate muonic force carrier (MFC) events resulting from scattering processes between muons and the detector material in high-energy physics colliders experiments. MFCs are bosons appearing in beyond-the-standard-model theoretical frameworks, which are candidates for dark matter. Empirical evidence suggests that Born machines can reproduce the marginal distributions and correlations of data sets from Monte Carlo simulations.