@article{ca980f590ec342baa0a266deac1ab93f,

title = "Boltzmann machine learning with a variational quantum algorithm",

abstract = "A Boltzmann machine is a powerful tool for modeling probability distributions that govern the training data. A thermal equilibrium state is typically used for the Boltzmann machine learning to obtain a suitable probability distribution. The Boltzmann machine learning consists of calculating the gradient of the loss function given in terms of the thermal average, which is the most time-consuming procedure. Here, we propose a method to implement the Boltzmann machine learning by using noisy intermediate-scale quantum devices. We prepare an initial pure state that contains all possible computational basis states with the same amplitude, and we apply a variational imaginary time simulation. Readout of the state after the evolution in the computational basis approximates the probability distribution of the thermal equilibrium state that is used for the Boltzmann machine learning. We perform the numerical simulations of our scheme and confirm that the Boltzmann machine learning works well. Our scheme leads to a significant step toward an efficient machine learning using quantum hardware.",

author = "Yuta Shingu and Yuya Seki and Shohei Watabe and Suguru Endo and Yuichiro Matsuzaki and Shiro Kawabata and Tetsuro Nikuni and Hideaki Hakoshima",

note = "Funding Information: We thank Dr. Muneki Yasuda for useful comments on the Boltzmann machine. We also thank Takashi Imoto and Atsuki Yoshinaga for valuable discussions. This work was supported by Leading Initiative for Excellent Young Researchers MEXT, Japan, and JST PRESTO (Grant No. JPMJPR1919), Japan. This work was partly supported by MEXT Q-LEAP (Grant No. JPMXS0118068682) and JST ERATO (Grant No. JPMJER1601). This paper is partly based on results obtained from a project, JPNP16007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO), Japan. S.W. was supported by Nanotech CUPAL, National Institute of Advanced Industrial Science and Technology (AIST). We performed the numerical calculations in Figs. and by using Qiskit, an open-source library for numerical simulations of quantum algorithms provided by Ref. . Publisher Copyright: {\textcopyright} 2021 American Physical Society. ",

year = "2021",

month = sep,

doi = "10.1103/PhysRevA.104.032413",

language = "English",

volume = "104",

journal = "Physical Review A",

issn = "2469-9926",

publisher = "American Physical Society",

number = "3",

}