Hardware-efficient quantum phase estimation via local control

TL;DR

This paper introduces a locally controlled quantum phase estimation method that reduces circuit depth, enabling spectral analysis of many-body quantum systems on current quantum hardware.

Contribution

It presents a novel approach to quantum phase estimation using only local controls, decreasing circuit depth and broadening applicability to various quantum states.

Findings

Reduces circuit depth compared to traditional methods

Provides efficient routines for phase measurement of the Loschmidt echo

Numerical simulations demonstrate practical feasibility

Abstract

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for an increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.