Adaptive Bayesian phase estimation for quantum error correcting codes

Abstract

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum states becomes more difficult since the number of parameters to be measured grows as well and finding efficient observables in order to estimate the parameters of the model becomes a crucial task. Here we propose a method relying on application of Bayesian inference that can be used to determine systematic, unknown phase shifts of multi-qubit states. This method offers important advantages as compared to Ramsey-type protocols. First, application of Bayesian inference allows the selection of an adaptive basis for the measurements which yields the optimal amount of information about the phase shifts of the state. Secondly, this method can process the outcomes of different observables at the same time. This leads to a substantial decrease in the resources needed for the estimation of phases, speeding up the state characterisation and optimisation in experimental implementations. The proposed Bayesian inference method can be applied in various physical platforms that are currently used as quantum processors.

arXiv comment23 pages including appendices, 11 color figures

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• Bayesian parameter estimation using Gaussian states and measurements
• Experimental Bayesian calibration of trapped ion entangling operations
• Determination of the asymptotic limits of adaptive photon counting measurements for coherent-state optical phase estimation
• Bayesian quantum phase estimation with fixed photon states
• Time-adaptive phase estimation
• Knowledge-dependent optimal Gaussian strategies for phase estimation