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arXiv · 1909.12250

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

Suguru Endo·Iori Kurata·Yuya O. Nakagawa
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Abstract

The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically-intractable systems, methods to simulate the Green's function with near-term quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green's function of a given Hamiltonian on near-term quantum computers. The first one makes use of a 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. We numerically simulated the Green's function of the Fermi-Hubbard model and demonstrated the validity of our proposals.

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Suguru Endo, Iori Kurata, Yuya O. Nakagawa. 2019-09-26. Calculation of the Green's function on near-term quantum computers. https://doi.org/10.1103/physrevresearch.2.033281

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