Fermionic-Adapted Shadow Tomography for dynamical correlation functions

TL;DR

This paper introduces Fermionic-Adapted Shadow Tomography (FAST), a new quantum measurement protocol that efficiently computes multiple dynamical correlation functions in many-body systems, reducing measurement complexity.

Contribution

The paper develops FAST protocols that reformulate dynamical correlation functions for efficient shadow tomography, improving measurement efficiency in quantum many-body analysis.

Findings

Enhances sample efficiency in measuring dynamical correlations.

Reduces number of measurement circuits by an order of magnitude.

Compatible with uncontrolled Hamiltonian simulation.

Abstract

Dynamical correlation functions are essential for characterizing the response of the quantum many-body systems to the external perturbation. As their calculation is classically intractible in general, quantum algorithms are promising in this aspect, but most rely on brute force measurement strategies that evaluate one body observable pair per circuit. In this work, we introduce Fermionic-Adapted Shadow Tomography (FAST) protocols, a new framework for the efficient calculation of multiple dynamical correlation functions. The key idea is to reformulate these functions into forms that are compatible with shadow tomography techniques. The circuits in our protocols require at most two-copy measurements with uncontrolled Hamiltonian simulation. We show that the proposed protocols enhance sample efficiency and/or reduce the number of measurement circuits by an order of one or two with respect to the number of qubits across a range of scenarios.