Abstract 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 an existing 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.
Abstract 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 an existing 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.
As the quantum computing community gravitates towards understanding the practical benefits of quantum computers, having a clear definition and evaluation scheme for assessing practical quantum advantage in the context of specific applications is paramount. Generative modeling, for example, is a widely accepted natural use case for quantum computers, and yet has lacked a concrete approach for quantifying success of quantum models over classical ones. In this work, we construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Using the sample-based approach proposed here, any generative model, from state-of-the-art classical generative models such as generative adversarial networks (GANs) to quantum models such as quantum circuit born machines, can be evaluated under the same conditions on a concrete well-defined framework. In contrast to other sample-based metrics for probing practical generalization, we leverage constrained optimization problems (e.g., cardinality-constrained problems) and use these discrete datasets to define specific metrics capable of unambiguously measuring the quality of the samples and the model's generalization capabilities for generating data beyond the training set, but still within the valid solution space. Additionally, our metrics can diagnose trainability issues such as mode collapse and overfitting, as we illustrate when comparing GANs to quantum-inspired models built out of tensor networks. Our simulation results show that our quantum-inspired models have up to a 68 times enhancement in generating unseen unique and valid samples compared to the GANs explored here, and a ratio of 61:2 for generating samples with better quality than those observed in the training set. We foresee these metrics as valuable tools for rigorously defining practical quantum advantage in the domain of generative modeling, where finding a winning model remains an ongoing challenge as new architectures are developed.
Although several models have been proposed towards assisting machine learning (ML) tasks with quantum computers, a direct comparison of the expressive power and efficiency of classical versus quantum models for datasets originating from real-world applications is one of the key milestones towards a quantum ready era. Here, we take a first step towards addressing this challenge by performing a comparison of the widely used classical ML models known as restricted Boltzmann machines (RBMs), against a recently proposed quantum model, now known as quantum circuit Born machines (QCBMs). Both models address the same hard tasks in unsupervised generative modeling, with QCBMs exploiting the probabilistic nature of quantum mechanics and a candidate for near-term quantum computers, as experimentally demonstrated in three different quantum hardware architectures to date. To address the question of the performance of the quantum model on real-world classical data sets, we construct scenarios from a probabilistic version out of the well-known portfolio optimization problem in finance, by using time-series pricing data from asset subsets of the S&P500 stock market index. It is remarkable to find that, under the same number of resources in terms of parameters for both classical and quantum models, the quantum models seem to have superior performance on typical instances when compared with the canonical training of the RBMs. Our simulations are grounded on a hardware efficient realization of the QCBMs on ion-trap quantum computers, by using their native gate sets, and therefore readily implementable in near-term quantum devices.
Quantum generative models harness the probabilistic nature of quantum mechanics to represent and learn complex distributions, offering a novel framework for both classical and quantum data modeling. This chapter introduces foundational architectures such as quantum circuit Born machines, quantum generative adversarial networks, and variational autoencoders, emphasizing their expressivity, training methods, and applications. We explore use cases ranging from anomaly detection to spectral function sampling and discuss key challenges including trainability, noise, and evaluation metrics. The chapter concludes by outlining opportunities for quantum advantage in generative tasks and highlighting emerging strategies for scalable, noise-resilient model training on near-term quantum devices.
Quantum generative modeling is a growing area of interest for industry-relevant applications. This work systematically compares a broad range of techniques to guide quantum computing practitioners when deciding which models and methods to use in their applications. We compare fundamentally different architectural ansatzes of parametric quantum circuits: (1) A continuous architecture, which produces continuous-valued data samples, and (2) a discrete architecture, which samples on a discrete grid. We also compare the performance of different data transformations: the min-max and the probability integral transforms. We use two popular training methods: (1) quantum circuit Born machines (QCBM), and (2) quantum generative adversarial networks (QGAN). We study their performance and tradeoffs as the number of model parameters increases, with a baseline comparison of similarly trained classical neural networks. The study is performed on six low-dimensional synthetic and two real financial data sets. Our two key findings are that: (1) For all data sets, our quantum models require similar or fewer parameters than their classical counterparts. In the extreme case, the quantum models require two orders of magnitude less parameters. (2) We empirically find that a variant of the discrete architecture, which learns the copula of the probability distribution, outperforms all other methods.
Combinatorial optimization is one of the key candidates in the race for practical quantum advantage. In this work, we introduce a new family of quantum-enhanced optimizers and demonstrate how quantum machine learning models known as quantum generative models can find lower minima than those found by means of stand-alone state-of-the-art classical solvers. We present two new quantum-enhanced optimization strategies. The first scheme leverages data points evaluated during the optimization search from any quantum or classical optimizer. In this scheme, we show how our quantum generative model boosts the performance of classical solvers in hard-to-solve instances where the classical solver is not capable of making progress as a stand-alone strategy. The second quantum optimization strategy works as a stand-alone solver. Here we show its superior performance when the goal is to find the best minimum within the least number of cost function evaluations. Under this setting, we benchmark our quantum-enhanced optimization strategies against several solvers, including Bayesian optimizers which are known to be one of the best competing solvers in such tasks. To illustrate our findings, these benchmarks are performed in the context of the portfolio optimization problem by constructing instances from the S&P 500 stock market index. We show that our quantum-inspired generative models based on tensor networks generalize to unseen candidates with lower cost function values than any of the candidates seen by the classical solvers. This is the first demonstration of the generalization capabilities of quantum generative models that brings real value in the context of an industrial-scale application.
Abstract 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.