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Optimal Quantum State Tomography with Noisy Gates

Violeta N. Ivanova-RohlingNiklas RohlingGuido Burkard
摘要
Quantum state tomography (QST) represents an essential tool for thecharacterization, verification, and validation (QCVV) of quantum processors.Only for a few idealized scenarios, there are analytic results for the optimalmeasurement set for QST. E.g., in a setting of non-degenerate measurements, anoptimal minimal set of measurement operators for QST has eigenbases which aremutually unbiased. However, in other set-ups, dependent on the rank of theprojection operators and the size of the quantum system, the optimal choice ofmeasurements for efficient QST needs to be numerically approximated. We havegeneralized this problem by introducing the framework of customized efficientQST. Here we extend customized QST and look for the optimal measurement set forQST in the case where some of the quantum gates applied in the measurementprocess are noisy. To achieve this, we use two distinct noise models: first,the depolarizing channel, and second, over- and under-rotation in single-qubitand to two-qubit gates (for further information, please see Methods). Wedemonstrate the benefit of using entangling gates for the efficient QSTmeasurement schemes for two qubits at realistic noise levels, by comparing thefidelity of reconstruction of our optimized QST measurement set to thestate-of-the-art scheme using only product bases.
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