Recent Advances for Quantum Neural Networks in Generative Learning

Abstract

Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relation and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

TeD-Q: a tensor network enhanced distributed hybrid quantum machine learning framework

“…Quantum GAN borrowed this idea and wishes to boost the performance by quantum computing [35,36]. While it is possible to use QNN in both the generative and discriminative networks, here, we adopt both the patch and non-patch quantum GAN methods where only the generative part is made quantum.…”

Do quantum circuit Born machines generalize?

“…These networks capture correlations within high-dimensional target distributions, often times having limited access to information, which makes generative modeling a much more difficult task compared to discriminative modeling [21,36,37]. Many kinds of generative models have been proposed in the literature, and often come with different architectures, training strategies, and limitations [6,38]. A few notable model families include generative adversarial networks [39], restricted Boltzmann machines (RBMs) [40], tensor network Born machines [41] and QCBMs [7].…”

“…In the pursuit of practical quantum advantage on classical data, unsupervised generative modeling tasks stand out as one of the most promising application candidates given their increased complexity compared to supervised ML tasks, and therefore a better target for seeking advantage with near-term quantum computers [5]. Many quantum generative models have been proposed with very little discussion around their learning potential in the context of generalization [6], despite its importance. One of the most popular quantum circuit families for generative tasks, known as quantum circuit Born machines (QCBMs) [7], have demonstrated remarkable capabilities in modeling target distributions for both toy and real-world datasets [7][8][9][10][11][12][13][14][15][16].…”

Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage

“…Despite the intrinsic theoretical advantages of quantum computers, the widespread adoption of quantum technologies will ultimately depend on the benefits they can offer for solving problems of high practical interest using these limited resources. To this end, parametrized quantum circuits (PQCs) [4][5][6] have been proposed as a promising formalism for leveraging nearterm quantum devices for the solution of problems in quantum chemistry [7][8][9], materials science [10], and quantum machine learning [11][12][13][14][15][16][17][18][19] applications which are difficult for classical algorithms.…”