TY - JOUR

T1 - Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers

AU - Matsumoto, Keisuke

AU - Shingu, Yuta

AU - Endo, Suguru

AU - Kawabata, Shiro

AU - Watabe, Shohei

AU - Nikuni, Tetsuro

AU - Hakoshima, Hideaki

AU - Matsuzaki, Yuichiro

N1 - Funding Information:
This work was supported by Leading Initiative for Excellent Young Researchers MEXT Japan and JST presto (Grant No. JPMJPR1919) Japan. S.W. was supported by Nanotech CUPAL, National Institute of Advanced Industrial Science and Technology (AIST). This paper was partly based on results obtained from a project, JPNP16007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO), Japan. We performed the numerical calculations in Figs. –, Figs. , and by using Qiskit, an open-source library for numerical simulations of quantum algorithms provided by Ref. .
Publisher Copyright:
© 2022 The Japan Society of Applied Physics.

PY - 2022/4

Y1 - 2022/4

N2 - The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-term quantum computers. However, the existing schemes require many copies of the Gibbs states to perform an extrapolation for the calculation of the partition function, which could be costly performed on the near-term quantum computers. We propose a scheme to calculate the Gibbs function with the imaginary time evolution. After preparing Gibbs states with different temperatures by using the imaginary time evolution, we measure the overlap between them on a quantum circuit, which allows us to calculate the Gibbs partition function. Our scheme requires only 2N qubits to calculate the Gibbs function of N qubits.

AB - The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-term quantum computers. However, the existing schemes require many copies of the Gibbs states to perform an extrapolation for the calculation of the partition function, which could be costly performed on the near-term quantum computers. We propose a scheme to calculate the Gibbs function with the imaginary time evolution. After preparing Gibbs states with different temperatures by using the imaginary time evolution, we measure the overlap between them on a quantum circuit, which allows us to calculate the Gibbs partition function. Our scheme requires only 2N qubits to calculate the Gibbs function of N qubits.

KW - Gibbs partition function

KW - NISQ

KW - quantum computer

UR - http://www.scopus.com/inward/record.url?scp=85127249176&partnerID=8YFLogxK

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U2 - 10.35848/1347-4065/ac5152

DO - 10.35848/1347-4065/ac5152

M3 - Article

AN - SCOPUS:85127249176

VL - 61

JO - Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes

JF - Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes

SN - 0021-4922

IS - 4

M1 - 042002

ER -