Measurement circuit ansatz: Naimark versus quantum neural-network measurements

Abstract:In this work, we present constructions of quantum circuits to implement general measurements on quantum hardware. Firstly, we investigate a quantum circuit ansatz by following the Naimark extension with a universal set of gates, such as controlled-NOT and single-qubit gates; we call it a {\it Naimark measurement}. We present a circuit ansatz framed by the Naimark extension, leaving single-qubit gates with parameters, and apply a classical optimizer to determine their parameters to approximate a desired quantum measurement. Secondly, we relax the Naimark measurement with quantum neural-network (QNN) circuits, employing parameterized quantum circuits. We present hybrid Naimark-QNN measurements by incorporating QNN circuits into Naimark measurements. Thirdly, we also consider fully QNN measurements with shallow parameterized circuits. Then, we compare the constructed measurement circuits, Naimark, hybrid Naimark-QNN, and fully QNN measurements, for strategies of state discrimination, such as minimum-error and maximum-confidence measurements. We demonstrate that QNN circuits can efficiently and effectively achieve near-optimal quantum measurements with fewer training iterations.

arXiv:2606.07376 [quant-ph]

(or arXiv:2606.07376v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.07376 Focus to learn more arXiv-issued DOI via DataCite

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