Open qubit parameter identification with bounded pulses

TL;DR

This paper presents a method for identifying parameters of an open qubit using minimal configurations and bounded control pulses, providing analytical reconstruction and error bounds for practical implementation.

Contribution

It introduces a minimal configuration protocol for open qubit parameter estimation with bounded pulses, including analytical solutions and error analysis for realistic conditions.

Findings

Parameters can be reconstructed analytically with ideal infinite-amplitude pulses.

Finite pulses introduce bounded estimation errors.

The method separates statistical and modeling uncertainties.

Abstract

We address the problem of parameter identification for a single open qubit subjected to relaxation and dephasing. Our approach is based on selecting a minimal set of carefully chosen qubit configurations that can be reliably prepared and measured in order to provide an interpretable methodology of parameter identification while potentially minimizing experimental overhead. The protocol relies on saturating control pulses to generate these configurations. In an idealized regime of infinite-amplitude pulses, we demonstrate that the parameters can be reconstructed analytically from the measured observables. We then consider large but finite pulses as a perturbation of this ideal regime and provide bounds on the estimation error introduced by the practical implementation. This framework allows us to separate the sources of uncertainty in the estimation procedure, distinguishing between statistical fluctuations arising from repeated measurements and modeling errors due to deviations from the ideal pulse regime.