Universal imaginary-time critical dynamics on a quantum computer

Abstract

Quantum computers promise a highly efficient approach to investigate quantum phase transitions, which describe abrupt changes between different ground states of many-body systems. At quantum critical points, the divergent correlation length and entanglement entropy render the ground state preparation difficult. In this work, we explore the imaginary-time evolution for probing the universal critical behavior as the universal information of the ground state can be extracted in the early-time relaxation process. We propose a systematic and scalable scheme to probe the universal behaviors via imaginary-time critical dynamics on quantum computers and demonstrate the validness of our approach by both numerical simulation and quantum hardware experiments. With the full form of the universal scaling function in terms of imaginary time, system size, and circuit depth, we successfully probe the universality by scaling analysis of the critical dynamics at an early time and with shallower quantum circuit depth. Equipped with quantum error mitigation, we also confirm the expected scaling behavior from experimental results on a superconducting quantum processor which stands as the first experimental demonstration on universal imaginary-time quantum critical dynamics.

5 pages, 4 figures and supplemental materials

References in corpus (4)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A class of quantum many-body states that can be efficiently simulated
• Hybrid quantum-classical algorithms and quantum error mitigation
• Neural network encoded variational quantum algorithms

Cited by in corpus (8)

• Unveiling quantum phase transitions from traps in variational quantum algorithms
• Imaginary-time Mpemba effect in quantum many-body systems
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Imaginary-time relaxation quantum critical dynamics in two-dimensional dimerized Heisenberg model
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Short-time critical dynamics in the classical cubic dimer model
• Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states