arXiv:2301.09363 · ACM Transactions on Quantum Computing
A Characterization of Quantum Generative Models
Carlos A. Riofrío, Oliver Mitevski, C. R. Jones, Florian Krellner, Aleksandar Vuckovic, Joseph A. Doetsch, Johannes Klepsch, Thomas Ehmer, André Luckow
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.
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.
Abstract Quantum generative adversarial networks (QGANs) have been studied in the context of quantum machine learning for several years, but there has not been yet a proposal for a fully QGAN with both, a quantum generator and discriminator. We introduce a fully QGAN intended for use with binary data. The architecture incorporates several features found in other classical and quantum machine learning models, which up to this point had not been used in conjunction. In particular, we incorporate classical noise reuploading in the generator, auxiliary qubits in the discriminator to enhance expressivity, and a direct connection between the generator and discriminator circuits, obviating the need to access the generator’s probability distribution. We show that, as separate components, the generator and discriminator perform as desired. We empirically demonstrate the expressive power of our model on both synthetic data as well as low energy states of an Ising model. Our demonstrations suggest that the model is not only capable of reproducing discrete training data, but also of potentially generalizing from it.
Generative quantum machine learning models are trained to deduce the probability distribution underlying a given dataset, and to produce new, synthetic samples from it. The majority of such models proposed in the literature, like the Quantum Circuit Born Machine (QCBM), fundamentally work on a binary level. Real-world data, however, is often numeric, requiring the models to translate between binary and continuous representations. We analyze how this transition influences the performance of quantum models and show that it requires the models to learn correlations that are solely an artifact of the way the data is encoded, and not related to the data itself. At the same time, structure of the original data, like continuity, can be obscured in the binary representation, hindering generalization. To mitigate these effects, we propose a strategy based on Gray-codes that can be implemented with essentially no overhead, conserves structures in the data, and avoids artificial correlations in situations in which the standard approach creates them. Considering datasets drawn from various low-dimensional probability distributions, we verify that, in most cases, QCBMs using the reflected Gray code learn faster and more accurately than those with standard binary code. This shows that, as complement to specifically tailored circuit ansätze or data pre-processing, binary encodings can be used to introduce inductive biases into generative machine learning models.
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.
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.
This paper investigates the application of Quantum Generative Adversarial Networks (QGANs) to data augmentation for machine learning. Traditional Generative Adversarial Networks (GANs) rely on classical neural networks, while this research explores leveraging quantum circuits as generators within a QGAN architecture. The core idea is to train a quantum generator to produce synthetic data samples, supplementing existing datasets with novel instances. The discriminator remains a classical neural network, tasked with distinguishing between real and generated data. We present a theoretical framework for this approach, outlining the mathematical formulation and key components. Specifically, we introduce the notation (x, s_1, s_2, ..., s_K) to represent data samples, generator states, and relevant parameters. The objective function for the QGAN is defined as minimizing the Jensen-Shannon divergence between the real and generated data distributions. The effectiveness of this approach is discussed, highlighting potential advantages and challenges. This work contributes to the emerging field of quantum machine learning and offers a novel strategy for improving the performance of machine learning models, particularly in scenarios with limited training data.
Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling joint distributions via copulas is well understood, it gets practically challenging to accurately model real data with many variables. In this paper, we show that any copula can be naturally mapped to a multipartite maximally entangled state. Thus, the task of learning joint probability distributions becomes the task of learning maximally entangled states. We prove that a variational ansatz we christen as a ``qopula'' based on this insight leads to an exponential advantage over classical methods of learning some joint distributions. As an application, we train a quantum generative adversarial network (QGAN) and a quantum circuit Born machine (QCBM) using this variational ansatz to generate samples from joint distributions of two variables in historical data from the stock market. We demonstrate our generative learning algorithms on trapped ion quantum computers from IonQ for up to eight qubits. Our experimental results show interesting findings such as the resilience against noise, outperformance against equivalent classical models and 20--1000 times less iterations required to converge as compared to equivalent classical models.