Keldysh-ETH quantum computation algorithm*

There is growing interest in implementing new quantum algorithms that can help us study strongly correlated systems on a quantum computer. Although understanding the properties of the ground state of a physical system is one of the most fundamental problems, here, we focus on the realization of quantum systems at a finite temperature that is described in terms of their Green's functions. We develop an algorithm that enables us to directly measure an equilibrium fermionic Green's function at finite temperature without requiring adiabatic state preparation or Gibbs state preparation. We propose an efficient and fast algorithm that can be applied for systems that satisfy
the eigenstate thermalization (ETH) hypothesis. The Green's functions can be shown to be exact at short times, and they deviate from the exact solution at increasingly longer times for larger systems. We also discuss some cooling ideas, which allow the system to reach even lower temperatures.