  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 finite temperature phase
diagram of the Kitaev model. 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 readily implemented on
current quantum processors. We further propose a protocol implementable with
superconducting or trapped ion quantum computers.
