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Stability of Classical Shadows under Gate-Dependent Noise.

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Classical shadows provide accurate quantum state estimation with Clifford circuits, but "magic" observables are sensitive to noise. Robust shadows can mitigate some errors but may introduce bias in specific noisy quantum computing scenarios.

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Area of Science:

  • Quantum information science
  • Quantum computing

Background:

  • Classical shadows estimate quantum states via randomized measurements.
  • Understanding noise impact on shadow estimation is vital for practical applications.

Purpose of the Study:

  • To analyze the stability of classical shadow protocols under realistic noise conditions.
  • To investigate the performance of robust shadows in mitigating noise.

Main Methods:

  • Theoretical analysis of shadow estimation protocols with Clifford unitaries.
  • Demonstration of noise effects on bounded stabilizer norm and
  • magic
  • observables.
  • Identification of average noise channels affecting shadow estimators.

Main Results:

  • Clifford-based classical shadows are stable under gate-dependent noise for bounded stabilizer norm observables.
  • Estimation of
  • magic
  • observables is highly susceptible to miscalibration errors, with exponential bias.
  • Robust shadows can introduce bias under gate-dependent noise, but their functionality is guaranteed in more general noise settings.

Conclusions:

  • Classical shadow protocols are robust for specific observables under Clifford operations and gate-dependent noise.
  • Careful consideration of observable types and noise models is necessary for reliable quantum state estimation.
  • Further research into noise characterization can refine quantum sensing and computation accuracy.