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.
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BibTeX
@misc{yun2026measurement,
title = {{Measurement circuit ansatz: Naimark versus quantum neural-network measurements}},
author = {Sung Won Yun and Thi Ha Kyaw and Joonwoo Bae},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.07376},
eprint = {2606.07376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.07376},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Measurement circuit ansatz: Naimark versus quantum neural-network measurements
AU - Sung Won Yun
AU - Thi Ha Kyaw
AU - Joonwoo Bae
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2606.07376
UR - https://arxiv.org/abs/2606.07376
AB - 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.
ER -