A circuit-differentiation framework for Green's functions on quantum computers

TL;DR

This paper introduces a quantum computing framework for calculating Green's functions using circuit differentiation, enabling efficient dynamical correlation computations in noisy and fault-tolerant regimes.

Contribution

It presents a novel circuit differentiation approach for Green's functions, including stochastic estimators that do not require additional qubits, demonstrated on spin and fermionic models.

Findings

Accurate dynamical correlations obtained under realistic noise.

Circuit derivatives directly map to Green's functions computations.

Stochastic estimators work without extra qubits.

Abstract

We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically designed circuit components, which we refer to as circuit perturbations, acting as a direct representation of the external perturbative force within the quantum circuit in a linear-response setting. The direct mapping between circuit derivatives and the computation of RGFs enables the use of a broad range of differentiation strategies. We provide two such examples, including a class of stochastic estimators which do not require extra qubit connectivity with respect to the underlying time-evolution operations. We demonstrate our approach on interacting spin and fermionic models, showing that accurate dynamical correlations can be obtained even under realistic noise assumptions. Finally, we outline how our proposal can be tied to efficient gradient-estimation techniques relevant for the fault-tolerant regime.