Robust multiparameter estimation using quantum scrambling

TL;DR

This paper introduces a quantum sensing protocol that uses scrambling dynamics to efficiently estimate many non-commuting, time-dependent signals simultaneously, even with control imperfections, achieving exponential parameter detection with optimal sensitivity scaling.

Contribution

It presents a novel multiparameter quantum sensing method leveraging scrambling dynamics, enabling efficient detection of numerous signals with robustness to errors and broad applicability.

Findings

Detects exponentially many parameters with system size

Maintains optimal sensitivity scaling despite imperfections

Applicable to various scrambling dynamics in quantum hardware

Abstract

We propose and analyze a versatile and efficient multiparameter quantum sensing protocol, which simultaneously estimates many non-commuting and time-dependent signals that are coherently or incoherently coupled to sensing particles. Even in the presence of control imperfections and readout errors, our approach can detect exponentially many parameters in the system size while maintaining the optimal scaling of sensitivity. To accomplish this, scrambling dynamics are leveraged to map distinct signals to unique patterns of bitstring measurements, which distinguishes a large number of signals without significant sensitivity loss. Based on this principle, we develop a computationally efficient protocol utilizing random global Clifford unitaries and evaluate its performance both analytically and numerically. Our protocol naturally extends to scrambling dynamics generated by random local Clifford circuits, local random unitary circuits (RUCs), and ergodic Hamiltonian evolution--commonly realized in near-term quantum hardware--and opens the door to applications ranging from precise noise benchmarking of quantum dynamics to learning time-dependent Hamiltonians.