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arXiv:2210.06103 · Physical Review Applied

Real-time adaptive estimation of decoherence timescales for a single qubit

Muhammad Junaid Arshad, Christiaan Bekker, Ben Haylock, Krzysztof Skrzypczak, Daniel White, Benjamin Griffiths, Joe Gore, Gavin W. Morley, Patrick S. Salter, Jason A. Smith, Inbar Zohar, Amit Finkler, Yoann Altmann, Erik M. Gauger, Cristian Bonato

Published Feb 13, 2024• 11 citations
arXivHTMLPDF

Abstract

Characterizing the time over which quantum coherence survives is critical for any implementation of quantum bits, memories, and sensors. The usual method for determining a quantum system’s decoherence rate involves a suite of experiments probing the entire expected range of this parameter, and extracting the resulting estimation in postprocessing. Here we present an adaptive multiparameter Bayesian approach, based on a simple analytical update rule, to estimate the key decoherence timescales ( T1 , T2∗ , and T2 ) and the corresponding decay exponent of a quantum system in real time, using information gained in preceding experiments. This approach reduces the time required to reach a given uncertainty by a factor up to an order of magnitude, depending on the specific experiment, compared to the standard protocol of curve fitting. A further speedup of a factor approximately 2 can be realized by performing our optimization with respect to sensitivity as opposed to variance. Published by the American Physical Society 2024

DOI
10.1103/physrevapplied.21.024026

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Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. It has been solved for some specific instances of the problem, but in general even numerical methods are not known. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe (which can be entangled with an auxiliary system), the optimal measurement, and the optimal estimator function. We leverage the formalism of higher-order operations to develop a method based on semidefinite programming that finds a protocol that is close to the optimal one with arbitrary precision. Crucially, our method is not restricted to any specific quantum evolution, cost function, or prior distribution, and thus can be applied to any estimation problem. Moreover, it can be applied to both single-parameter or multiparameter estimation tasks. We demonstrate our method with three examples, consisting of unitary phase estimation, thermometry in a bosonic bath, and multiparameter estimation of an SU(2) transformation. Exploiting our methods, we extend several results from the literature. For example, in the thermometry case, we find the optimal protocol at any finite time and quantify the usefulness of entanglement. Published by the American Physical Society 2024
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Abstract The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework.
Environmental fluctuations degrade the performance of solid-state qubits but can in principle be mitigated by real-time Hamiltonian estimation down to timescales set by the estimation efficiency. We implement a physics-informed and an adaptive Bayesian estimation strategy and apply them in real time to a semiconductor spin qubit. The physics-informed strategy propagates a probability distribution inside the quantum controller according to the Fokker-Planck equation, appropriate for describing the effects of nuclear spin diffusion in gallium arsenide. Evaluating and narrowing the anticipated distribution by a predetermined qubit probe sequence enables improved dynamical tracking of the uncontrolled magnetic field gradient within the singlet-triplet qubit. The adaptive strategy replaces the probe sequence by a small number of qubit probe cycles, with each probe time conditioned on the previous measurement outcomes, thereby further increasing the estimation efficiency. The combined real-time estimation strategy efficiently tracks low-frequency nuclear spin fluctuations in solid-state qubits, and can be applied to other qubit platforms by tailoring the appropriate update equation to capture their distinct noise sources. Published by the American Physical Society 2024