Bayesian Quantum Noise Spectroscopy

TL;DR

This paper introduces a Bayesian approach to quantum noise spectroscopy, framing it as a statistical estimation problem, which improves upon existing methods by allowing the incorporation of assumptions to make the problem solvable.

Contribution

The paper develops a Bayesian framework for quantum noise spectroscopy, providing a systematic way to incorporate assumptions and improve estimation accuracy.

Findings

Bayesian method outperforms other numerical techniques in noise spectroscopy

The approach effectively incorporates prior assumptions to solve ill-posed problems

Demonstrates improved reliability and interpretability over ad-hoc solutions

Abstract

As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is often never determined. Thus it is unclear when the method will succeed or whether one should trust the solution obtained. Here we propose to treat the problem from the point of view of statistical estimation theory. We develop a Bayesian solution to the problem which allows one to easily incorporate assumptions which render the problem solvable. We compare several numerical techniques for noise spectroscopy and find the Bayesian approach to be superior in many respects.