Qudit-native measurement protocol for dynamical correlations using Hadamard tests

TL;DR

This paper introduces a modified Hadamard test protocol for measuring dynamical correlations in qudit systems, overcoming previous limitations for qubits, and demonstrates its effectiveness through numerical benchmarks.

Contribution

The authors develop a qudit-native measurement protocol for dynamical correlations that extends Hadamard tests beyond qubits, enabling broader experimental applications.

Findings

Numerical benchmarking shows improved signal-to-noise ratio.

Protocol successfully applied to quench dynamics in a spin-1 XXZ chain.

Method is compatible with various quantum platforms.

Abstract

Dynamical correlations reveal important out-of-equilibrium properties of the underlying quantum many-body system, yet they are notoriously difficult to measure in experiments. While measurement protocols for dynamical correlations based on Hadamard tests for qubit quantum devices exist, they do not straightforwardly extend to qudits. Here, we propose a modified protocol to overcome this limitation by decomposing qudit observables into unitary operations that can be implemented and probed in a quantum circuit. We benchmark our algorithm numerically at the example of quench dynamics in a spin-1 XXZ chain with finite shot noise and demonstrate advantages in terms of the signal-to-noise ratio over established protocols based on linear response. Our scheme can readily be implemented on various platforms and offers a wide range of applications like variational quantum optimization and probing thermalization in many-body systems.