
Variational quantum simulation of thermal statistical states on a superconducting quantum processer
XueYi Guo(郭学仪), ShangShu Li(李尚书), Xiao Xiao(效骁), ZhongCheng Xiang(相忠诚), ZiYong Ge(葛自勇), HeKang Li(李贺康), PengTao Song(宋鹏涛), Yi Peng(彭益), Zhan Wang(王战), Kai Xu(许凯), Pan Zhang(张潘), Lei Wang(王磊), DongNing Zheng(郑东宁), and Heng Fan(范桁)
Chin. Phys. B,
2023, 32 (1):
010307.
DOI: 10.1088/16741056/aca7f3
Quantum computers promise to solve finitetemperature properties of quantum manybody systems, which is generally challenging for classical computers due to high computational complexities. Here, we report experimental preparations of Gibbs states and excited states of Heisenberg $XX$ and $XXZ$ models by using a 5qubit programmable superconducting processor. In the experiments, we apply a hybrid quantumclassical algorithm to generate finite temperature states with classical probability models and variational quantum circuits. We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits, which enable us to prepare excited states at arbitrary energy density. We demonstrate that the approach has a selfverifying feature and can estimate fundamental thermal observables with a small statistical error. Based on numerical results, we further show that the time complexity of our approach scales polynomially in the number of qubits, revealing its potential in solving largescale problems.

