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Algorithmic Quantum Simulations of Quantum Thermodynamics

Yangsen Ye1,2,*, Jue Nan3,4,5,*, Dong Chen3,4,5,*, Torsten V. Zache6,7, Qingling Zhu2,8, Yiming Zhang1,2, Yuan Li1,2, Xiawei Chen2, Chong Ying2,8 et al.

Chen Zha2,8, Sirui Cao1,2, Shaowei Li2,8, Shaojun Guo1,2, Haoran Qian1,2, Hao Rong1,2, Yulin Wu1,2, Kai Yan2,8, Feifan Su2,8, Hui Deng1,2,8, Yu Xu2,8, Jin Lin2,8, Ming Gong1,2,8, Fusheng Chen2,8, Gang Wu1,8, Yong-Heng Huo1,2,8, Chao-Yang Lu1,2,8, Cheng-Zhi Peng1,2,8, Xiaobo Zhu1,2,8,9, Xiaopeng Li3,4,5,8,†, and Jian-Wei Pan1,2,8,‡

  • *These authors contributed equally to this work.
  • †Contact author: xiaopeng_li@fudan.edu.cn
  • ‡Contact author: pan@ustc.edu.cn

Phys. Rev. Lett. 137, 130603 – Published 23 September, 2026

DOI: https://doi.org/10.1103/n7tv-p5bp

Abstract

Characterizing quantum phases of matter at finite temperature is essential for understanding complex materials and large-scale thermodynamic phenomena. Here, we develop algorithmic protocols for simulating quantum thermodynamics on quantum hardware through quantum kernel function expansion (QKFE), producing the free energy as an analytic function of temperature with uniform convergence. These protocols are demonstrated by simulating transverse field Ising and XY models with superconducting qubits. In both analog and digital implementations of the QKFE algorithms, we exhibit quantitative agreement of our quantum simulation experiments with the exact results. Our approach provides a general framework for computing thermodynamic potentials on programmable quantum devices, granting access to key thermodynamic properties such as entropy, heat capacity, and criticality, with far-reaching implications for material design and drug development.

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