Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous variable for simulating quantum systems at finite temperatures. Our algorithm has a time complexity scaling polynomially with the inverse temperature and the desired accuracy. We demonstrate the quantum algorithm by simulating a finite temperature phase diagram of the quantum Ising and Kitaev models. It is found that the important crossover phase diagram of the Kitaev ring can be accurately simulated by a quantum computer with only a few qubits and thus the algorithm may be implementable on current quantum processors. We further propose a protocol with superconducting or trapped ion quantum computers.
RESEARCH
Continuous-Variable Assisted Thermal Quantum Simulation
School of Physics and Telecommunication Engineering/Achievements 2021-07-13 16:54:50 From：School of Physics and Telecommunication Engineering Hits： Favorite
Continuous-Variable Assisted Thermal Quantum Simulation
Dan-Bo Zhang, Guo-Qing Zhang, Zheng-Yuan Xue, Shi-Liang Zhu, and Z. D. Wang
Phys. Rev. Lett. 127, 020502 – Published 8 July 2021
ABSTRACT
Figure 1
An illustration of preparing quantum thermal state ρ(β) from N copies of Bell states, through coupling the system with a qumode by unitary evolution e−iH^p. The qumode is initialed at the resource state |R(β)⟩ and is finally projected onto |0⟩q. Thermal state ρ(β) is obtained by discarding (tracing out) the additional N ancillary qubits.
Figure 2
Performance of preparing thermal states of the single qubit with two different approaches: β (˜β) stands for results from TQS (adaptive TQS).
Figure 3
Finite temperature phase diagram of the one-dimensional Kitaev ring and quantum Ising model.
Figure 4
Simulation of crossover temperature for the Kitaev ring in the quantum critical regime with adaptive TQS. (a) Crossover temperatures that use different truncating of photon number Nc for the resource state |R(β=4)⟩.(b) Crossover temperature for different lattice sizes, L=2, 3, 4, 5.
