Quantum Feedback Protocol for Approximating Single-Body Green's Functions at Finite Temperature

We present a quantum feedback algorithm that aims to approximate single-body Green's functions at finite temperature. Extracting a single particle Green's function from a quantum computer is a well known process, but if one is interested in thermal properties the challenges and resources necessary for full Gibbs state preparation are generally too expensive for these machines in the near future. Here, we examine how sampling from more easily preparable states can yield precise approximations to single-particle Green's functions at finite temperature. We also show, through a feedback mechanism, that one can test for convergence and extract the effective temperature of the system being simulated. Further, we compare the trade-offs of different approaches to make these techniques applicable on near term devises. We draw on the ideas of the Eigenstate Thermalization Hypothesis as well as specific properties of Green's functions and use a family of 1-D Fermi-Hubbard models as our test case.