Hybrid quantum-classical approach for coupled-cluster Green's function theory

TL;DR

This paper presents a hybrid quantum-classical method for calculating Green's functions in many-body systems, reducing quantum resource requirements and outperforming classical approaches in the context of the Anderson impurity model.

Contribution

It introduces a quantum-classical implementation of the coupled-cluster Green's function method that avoids explicit ground state preparation, applicable to various models including the AIM.

Findings

Achieves an order of magnitude reduction in quantum gate complexity compared to classical methods.

Demonstrates applicability to the Anderson impurity model.

Requires $T$ gates scaling as $O(N^5)$ per time step, improving over classical $O(N^6)$ complexity.

Abstract

The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of $T$ gates that grows as $ \mathcal{O} \left(N^5 \right)$ per time step to calculate the impurity Green's function in the time domain, where $N$ is the total number of energy levels in the AIM. Since the number of $T$ gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requires $ \mathcal{O} \left(N^6 \right)$ computational resources per time step.