Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy

• URL: http://arxiv.org/abs/2205.04730v1
• Date: Tue, 10 May 2022 08:05:59 GMT
• Title: Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy
• Authors: Yuxuan Du, Zhuozhuo Tu, Bujiao Wu, Xiao Yuan, Dacheng Tao
• Abstract summary: We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
• Score: 67.02951777522547
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The intrinsic probabilistic nature of quantum mechanics invokes endeavors of designing quantum generative learning models (QGLMs) with computational advantages over classical ones. To date, two prototypical QGLMs are quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs), which approximate the target distribution in explicit and implicit ways, respectively. Despite the empirical achievements, the fundamental theory of these models remains largely obscure. To narrow this knowledge gap, here we explore the learnability of QCBMs and QGANs from the perspective of generalization when their loss is specified to be the maximum mean discrepancy. Particularly, we first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution and the quantum kernels are employed. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states. This bound can be further employed to seek potential quantum advantages in Hamiltonian learning tasks. Numerical results of QGLMs in approximating quantum states, Gaussian distribution, and ground states of parameterized Hamiltonians accord with the theoretical analysis. Our work opens the avenue for quantitatively understanding the power of quantum generative learning models.

Related papers

• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Advantages of quantum mechanics in the estimation theory [0.0]
  In quantum theory, the situation with operators is different due to its non-commutativity nature. We formulate, with complete generality, the quantum estimation theory for Gaussian states in terms of their first and second moments.
  arXiv  Detail & Related papers  (2022-11-13T18:03:27Z)
• Deterministic and random features for large-scale quantum kernel machine [0.9404723842159504]
  We show that the quantum kernel method (QKM) can be made scalable by using our proposed deterministic and random features. Our numerical experiment, using datasets including $O(1,000) sim O(10,000)$ training data, supports the validity of our method.
  arXiv  Detail & Related papers  (2022-09-05T13:22:34Z)
• Recent Advances for Quantum Neural Networks in Generative Learning [98.88205308106778]
  Quantum generative learning models (QGLMs) may surpass their classical counterparts. We review the current progress of QGLMs from the perspective of machine learning. We discuss the potential applications of QGLMs in both conventional machine learning tasks and quantum physics.
  arXiv  Detail & Related papers  (2022-06-07T07:32:57Z)
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments [5.774827369850958]
  Recent efforts highlight the development of quantum algorithms based upon quantum computed Hamiltonian moments. This tutorial review focuses on the typical ways of computing Hamiltonian moments using quantum hardware and improving the accuracy of the estimated state energies.
  arXiv  Detail & Related papers  (2021-09-27T04:24:19Z)
• Quantum Federated Learning with Quantum Data [87.49715898878858]
  Quantum machine learning (QML) has emerged as a promising field that leans on the developments in quantum computing to explore large complex machine learning problems. This paper proposes the first fully quantum federated learning framework that can operate over quantum data and, thus, share the learning of quantum circuit parameters in a decentralized manner.
  arXiv  Detail & Related papers  (2021-05-30T12:19:27Z)
• Towards understanding the power of quantum kernels in the NISQ era [79.8341515283403]
  We show that the advantage of quantum kernels is vanished for large size datasets, few number of measurements, and large system noise. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
  arXiv  Detail & Related papers  (2021-03-31T02:41:36Z)
• Experimental Quantum Generative Adversarial Networks for Image Generation [93.06926114985761]
  We experimentally achieve the learning and generation of real-world hand-written digit images on a superconducting quantum processor. Our work provides guidance for developing advanced quantum generative models on near-term quantum devices.
  arXiv  Detail & Related papers  (2020-10-13T06:57:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.