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

2011/02/28 by Alexandr Sergeevich, Anushya Chandran, Joshua Combes +2 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Basis (linear algebra) #Exponential function #Geometry #Hamiltonian (control theory) #Mathematical analysis #Mathematical optimization #Mathematics #Mean squared error #Physics #Power law #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Scaling #Statistical physics #Statistics #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physreva.84.052315

published as Phys. Rev. A 84, 052315 (2011) · 5 pages, 3 figures, 1 table. Published version

openalex publication_date 2011/11/15 · arxiv created 2011/11/23 · arxiv updated 2011/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 \ensuremath∼N^\ensuremath-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(\ensuremath-0.3N). That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in N.

Citations

• Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate
• Quantum measurement of a mesoscopic spin ensemble
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Adaptive Homodyne Measurement of Optical Phase
• Identifying an experimental two-state Hamiltonian to arbitrary accuracy
• Experimental Hamiltonian identification for controlled two-level systems
• Optimal States and Almost Optimal Adaptive Measurements for Quantum Interferometry
• Diluted maximum-likelihood algorithm for quantum tomography
• Quantum Algorithms Revisited
• Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

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• Efficient Estimation of Resonant Coupling between Quantum Systems
• Maximizing Information on the Environment by Dynamically Controlled Qubit Probes