PNNL

Abstract

The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of dynamics 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 a wide range of models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of T gates that grows as O(N^5) 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. For comparison, a classical CCGF calculation of the same order would require computational resources that grow as O(N^6)per time step.