Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis

TL;DR

This paper demonstrates that adaptive measurement strategies in a fixed basis can exponentially improve the precision of qubit Hamiltonian estimation, outperforming traditional Fourier-based methods.

Contribution

It introduces an adaptive Bayesian measurement scheme that achieves exponential scaling in the number of measurements for Hamiltonian parameter estimation.

Findings

Adaptive Bayesian algorithm yields near exponential MSE reduction.

Fixed basis measurements suffice for exponential scaling.

Fourier-based schemes only achieve polynomial error decrease.

Abstract

We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean square error (MSE) that decreases at best as a power law ~N^{-2} in the number of measurements N. By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to \exp(-0.3 N). That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in N.