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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Experimental Quantum State Measurement with Classical Shadows.

Ting Zhang1, Jinzhao Sun2,3, Xiao-Xu Fang1

  • 1School of Physics, Shandong University, Jinan 250100, China.

Physical Review Letters
|December 3, 2021
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Summary
This summary is machine-generated.

This study experimentally validates a quantum measurement technique called classical shadows. This efficient method uses fewer measurements to predict quantum state properties, crucial for quantum computing advancements.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Communication

Background:

  • Efficiently extracting classical properties from quantum states is vital for quantum computing and communication algorithms.
  • A theoretical framework by Huang, Kueng, and Preskill proposed classical shadows for predicting multiple state functions with minimal measurements.
  • This scheme offers a size-independent, information-theoretically optimal approach to quantum state characterization.

Purpose of the Study:

  • To experimentally investigate the feasibility of the classical shadows protocol in realistic, noisy quantum systems.
  • To assess the performance of different classical shadow measurement strategies (uniform, biased, derandomized) compared to conventional methods.
  • To demonstrate the estimation of nonlinear functions and analyze entanglement using classical shadows.

Main Methods:

  • Preparation of a four-qubit Greenberger-Hormann-Zeilinger (GHZ) state.
  • Implementation of uniform, biased, and derandomized classical shadow measurement protocols.
  • Comparison with conventional sequential measurement strategies utilizing importance sampling or observable grouping.
  • Estimation of expectation values for multiple observables and Hamiltonians.
  • Demonstration of nonlinear function estimation and entanglement analysis.

Main Results:

  • Experimental verification of the classical shadows scheme's efficacy in a realistic setting with noise and finite measurements.
  • Demonstrated superior performance of derandomized classical shadows over conventional methods for estimating multiple functions.
  • Successful estimation of expectation values and nonlinear functions, validating the protocol's versatility.
  • Analysis of the prepared GHZ state's entanglement properties.

Conclusions:

  • The experimental results confirm the practical utility of classical shadows, particularly derandomized versions, for characterizing quantum states.
  • This work highlights the potential of classical shadows for efficient quantum state estimation on noisy intermediate-scale quantum (NISQ) hardware.
  • The findings pave the way for more efficient quantum algorithms and enhanced quantum information processing capabilities.