Calculation of the Green’s function on near-term quantum computers

The Green’s function plays a crucial role to study the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in near term is expected to enable us to compute energy spectrum and energy eigenstates of such classically-intractable systems, the methods to simulate the Green’s function with near-term quantum algorithms have not been proposed yet.

Researchers at QunaSys, a Japan startup, with collaboration of the University of Tokyo, have proposed two methods to calculate the Green’s function of a given Hamiltonian on near-term quantum computers. The first one makes use of the variational dynamics simulation of quantum systems and computes the dynamics of the Green’s function in real time directly. The second one utilizes the Lehmann representation of the Green’s function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with near-term quantum computers. They numerically simulated the Green’s function of the Hubbard model and demonstrated the validity of their proposals.

A part of the numerical simulations in this work was done on Microsoft Azure Virtual Machines. (University of Tokyo)

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