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

Keisuke Matsumoto, Yuta Shingu, Suguru Endo, Shiro Kawabata, Shohei Watabe, Tetsuro Nikuni, Hideaki Hakoshima, Yuichiro Matsuzaki

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number042002
JournalJapanese Journal of Applied Physics
Issue number4
Publication statusPublished - 2022 Apr
Externally publishedYes


  • Gibbs partition function
  • NISQ
  • quantum computer

ASJC Scopus subject areas

  • Engineering(all)
  • Physics and Astronomy(all)


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