Heisenberg-limited metrology with perturbing interactions

TL;DR

This paper demonstrates that Heisenberg-limited quantum metrology can be achieved with GHZ-like states even in the presence of complex local interactions, using efficient classical algorithms for feedback.

Contribution

It introduces a protocol for Heisenberg-limited metrology under local interactions, utilizing classical computation methods applicable in various dimensions.

Findings

Achieves Heisenberg limit with local interactions during measurement.

Uses classical algorithms for feedback in quantum metrology.

Provides efficient sampling algorithms for short-time quantum dynamics.

Abstract

We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in the presence of generic spatially local, possibly strong interactions during the measurement process. An explicit protocol, which relies on single-qubit measurements and feedback based on polynomial-time classical computation, achieves the Heisenberg limit. In one dimension, matrix product state methods can be used to perform this classical calculation, while in higher dimensions the cluster expansion underlies the efficient calculations. The latter approach is based on an efficient classical sampling algorithm for short-time quantum dynamics, which may be of independent interest.