Coarse-grained quantum state tomography with optimal POVM construction

• URL: http://arxiv.org/abs/2404.06285v1
• Date: Tue, 9 Apr 2024 13:11:27 GMT
• Title: Coarse-grained quantum state tomography with optimal POVM construction
• Authors: Donghun Jung, Young-Wook Cho, Yosep Kim, Junghyun Lee,
• Abstract summary: We introduce a novel approach to reconstruct the target density matrix from a comprehensive set of Positive Operator-Valued Measures (POVM) We improve the robustness and stability of CG state tomography (QST) by optimizing the POVM set to achieve a generalized symmetric informationally complete (GSIC) POVM. We discuss a more efficient construction of N-qubit CG-QST without exponential increases in two-qubit or circuit depth per measurement.
• Score: 2.985603723386298
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Constructing an integrated large-scale qubit system of realistic size requires addressing the challenge of physical crowding among qubits. This constraint poses an issue of coarse-grained (CG) measurement, wherein information from the multi-qubit system is collectively gathered. In this work, we introduce a novel approach to reconstruct the target density matrix from a comprehensive set of Positive Operator-Valued Measures (POVM) using a Parameterized Quantum Circuit (PQC) under the constraint of CG measurement. We improve the robustness and stability of CG quantum state tomography (QST) by optimizing the POVM set to achieve a generalized symmetric informationally complete (GSIC) POVM through maximization of the von Neumann entropy. This optimized construction of CG-POVMs is scalable to an N-qubit system. We further discuss a more efficient construction of N-qubit CG-QST without exponential increases in two-qubit gates or circuit depth per measurement. Our scheme offers a viable pathway towards a detector-efficient large-scale solid-state embedded qubit platform by reconstructing crucial quantum information from collective measurements.

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