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arXiv:2207.10327 · Automatica

On the regularization and optimization in quantum detector tomography

Shuixin Xiao, Yuanlong Wang, Jun Zhang, Daoyi Dong, Shota Yokoyama, Ian R. Petersen, Hidehiro Yonezawa

Published Jun 17, 2023• 6 citations
arXivHTMLPDF
DOI
10.1016/j.automatica.2023.111124

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Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we design optimal probe states for detector estimation based on the minimum upper bound of the mean squared error (UMSE) and the maximum robustness. We establish the minimum UMSE and the minimum condition number for quantum detectors and provide concrete examples that can achieve optimal detector tomography. In order to enhance estimation precision, we also propose a two-step adaptive detector tomography algorithm and investigate how this adaptive strategy can be used to achieve efficient estimation of quantum detectors. Moreover, the superposition of coherent states are used as probe states for quantum detector tomography and the estimation error is analyzed. Numerical results demonstrate the effectiveness of both the proposed optimal and adaptive quantum detector tomography methods.
We present a technique for performing quantum detector tomography (QDT) of phase insensitive quantum detectors, a category under which many detectors of interest fall under, using gradient descent-based optimization to learn the positive operator-valued measure (POVM) that best describes the data collected using the detector under study. We numerically benchmark our method against constrained convex optimization (CCO) and show that it reaches higher or comparable reconstruction fidelity in much less time even in the presence of noise and limited probe state resources. We also present a possible extension of our approach to the phase sensitive case via a parametrization of POVMs on the complex Stiefel manifold which enables gradient based optimization restricted to this manifold.