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

Alexandr Sergeevich, Anushya Chandran, Joshua Combes, Stephen D. Bartlett, and Howard M. Wiseman

Phys. Rev. A 84, 052315 – Published 15 November 2011

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 $\sim N^{- 2}$ 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 $N$ .

Received 1 March 2011

DOI:https://doi.org/10.1103/PhysRevA.84.052315

Authors & Affiliations

Alexandr Sergeevich¹, Anushya Chandran^2,3, Joshua Combes^2,4, Stephen D. Bartlett¹, and Howard M. Wiseman^2,*

¹Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney 2006, Australia
²ARC Centre for Quantum Computation and Communication Technology, and Centre for Quantum Dynamics, Griffith University, Brisbane 4111, Australia
³Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
⁴Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA

^*H.Wiseman@griffith.edu.au

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Vol. 84, Iss. 5 — November 2011

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