Improved Quantum Sensing by Spectral Design

TL;DR

This paper presents a spectral engineering approach using unitary control to enhance quantum parameter estimation, demonstrating improved accuracy through spectral manipulation techniques.

Contribution

It introduces a method for spectral design via unitary control that simplifies spectral manipulation and improves quantum sensing precision.

Findings

Spectral manipulation simplifies to elementary switching operations for commuting Hamiltonians.

Any desired energy level spacing can be achieved, possibly reducing spectral range.

Spectral modifications can be expressed as convex combinations of original eigenvalues.

Abstract

We investigate how unitary control can improve parameter estimation by designing the effective spectrum of the imprinting Hamiltonian. We show that, for commuting Hamiltonians, the general problem of spectral manipulation via unitary control simplifies to a finite sequence of elementary switching operations. Furthermore, we demonstrate that any desired relative spacing of energy levels can be achieved, although this may come at the cost of a reduced spectral range. We also show that any modified spectrum can be expressed as a convex combination of the original eigenvalues, with the convex weights forming a bi-stochastic matrix. Through several single-parameter estimation examples, we demonstrate that our spectral engineering method substantially enhances estimation accuracy.