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arXiv · 2303.15667

Computation of Green's function by local variational quantum compilation

Shota Kanasugi·Shoichiro Tsutsui·Yuya O. Nakagawa·Kazunori Maruyama·Hirotaka Oshima·Shintaro Sato
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Abstract

Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum computers may enable us to compute the Green's function with high accuracy even for classically-intractable large-scale systems. Here, we propose an efficient method to compute the real-time Green's function based on the local variational quantum compilation (LVQC) algorithm, which simulates the time evolution of a large-scale quantum system using a low-depth quantum circuit constructed through optimization on a smaller-size subsystem. Our method requires shallow quantum circuits to calculate the Green's function and can be utilized on both near-term noisy intermediate-scale and long-term fault-tolerant quantum computers depending on the computational resources we have. We perform a numerical simulation of the Green's function for the one- and two-dimensional Fermi-Hubbard model up to $4\times4$ sites lattice (32 qubits) and demonstrate the validity of our protocol compared to a standard method based on the Trotter decomposition. We finally present a detailed estimation of the gate count for the large-scale Fermi-Hubbard model, which also illustrates the advantage of our method over the Trotter decomposition.

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Shota Kanasugi, Shoichiro Tsutsui, Yuya O. Nakagawa, Kazunori Maruyama, Hirotaka Oshima, Shintaro Sato. 2023-03-28. Computation of Green's function by local variational quantum compilation. https://doi.org/10.1103/physrevresearch.5.033070

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