Parameter Estimation with Mixed-State Quantum Computation

TL;DR

This paper introduces a quantum algorithm that leverages deterministic quantum computation with one bit to estimate parameters at the quantum metrology limit, improving precision through adaptive Bayesian methods and dynamical decoupling.

Contribution

It presents a novel quantum algorithm for parameter estimation at the quantum metrology limit using a one-bit quantum computation model with adaptive techniques.

Findings

Achieves parameter estimation with variance decreasing proportionally to evolution time.

Extends the method to multiple parameters using dynamical-decoupling.

Addresses discrete-time evolution and reference-frame alignment scenarios.

Abstract

We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$, we estimate $\theta$ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of $\theta$ whose variance has been decreased in proportion to the time of evolution under H. For the problem of estimating several parameters, we implement dynamical-decoupling techniques and use the results of single parameter estimation. The cases of discrete-time evolution and reference-frame alignment are also discussed within the adaptive approach.