Effective calculation of the Green's function in the time domain on near-term quantum processors

TL;DR

This paper introduces an improved quantum algorithm for calculating Green's functions in the time domain, reducing controlled operations and enabling exact time propagation on near-term quantum processors for small Hubbard models.

Contribution

The authors develop a novel protocol that minimizes controlled operations in quantum Green's function calculations and demonstrates its implementation on real superconducting quantum hardware.

Findings

Significant reduction in controlled operations compared to previous methods

Exact time propagation achieved for 2-site Hubbard model on quantum hardware

Applicable to 2-, 3-, and 4-site Hubbard models

Abstract

We propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models. This novel protocol significantly reduces the number of controlled operations when compared to those previously suggested in literature. Such reduction is quite remarkable when considering the 2-site Hubbard model, for which we show that it is possible to obtain the exact time propagation of the $|N\pm 1\rangle$ states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.