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Reliable Optimization of Arbitrary Functions over Quantum Measurements.

Jing Luo1, Jiangwei Shang1

  • 1Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China.

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|February 25, 2023
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Summary
This summary is machine-generated.

This study introduces reliable algorithms for optimizing quantum measurements, crucial for quantum information processing. The new methods efficiently find optimal values for various functions, enhancing quantum technologies.

Keywords:
Gilbert’s algorithmconvex optimizationnonconvex optimizationquantum measurement

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Area of Science:

  • Quantum Information Science
  • Quantum Measurement Theory
  • Computational Physics

Background:

  • Quantum measurements are fundamental to quantum information processing, bridging classical and quantum mechanics.
  • Optimizing arbitrary functions of quantum measurements is a key challenge in diverse quantum applications.
  • Existing methods may struggle with the complexity and non-convexity of certain optimization landscapes.

Purpose of the Study:

  • To develop reliable algorithms for optimizing arbitrary functions over the space of quantum measurements.
  • To provide a general framework applicable to various quantum information tasks.
  • To demonstrate the effectiveness of the proposed algorithms for both convex and non-convex functions.

Main Methods:

  • Combining Gilbert's algorithm for convex optimization with gradient-based algorithms.
  • Developing a hybrid approach to handle diverse function types.
  • Testing algorithms on benchmark problems in quantum information.

Main Results:

  • Demonstrated reliable optimization of arbitrary functions of quantum measurements.
  • Successfully applied algorithms to problems like quantum measurement tomography and channel capacity calculations.
  • Validated algorithm efficacy on both convex and non-convex optimization tasks.

Conclusions:

  • The proposed hybrid algorithms offer a robust solution for optimizing quantum measurement functions.
  • This work provides a valuable tool for advancing quantum information processing and related fields.
  • The developed methods are broadly applicable, enhancing the practical utility of quantum technologies.