Quantum Feedback Protocol for Calculating Single-Particle Green's Functions at Finite Temperature

Drawing on the eigenstate thermalization hypothesis, we present a quantum feedback algorithm that approximates single-particle Green's functions at finite temperature. Measuring a single-particle Green's function from a thermal state on a quantum computer is a well known procedure, but the challenges and resources needed for full Gibbs state preparation are generally too expensive for practical simulation in the near future. We examine how sampling from more easily prepared states yields accurate approximations to single-particle Green's functions at finite temperature. We employ an additional feedback mechanism, that tests for convergence and extracts the effective temperature of the system being simulated. We also compare the trade-offs of different approaches to make these techniques applicable on near term devices.