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Nonclassicality and Coherent Error Detection via Pseudo-Entropy.

Assaf Katz1, Shalom Bloch1, Eliahu Cohen1

  • 1Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel.

Entropy (Basel, Switzerland)
|November 26, 2025
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Summary
This summary is machine-generated.

We introduce pseudo-entropy to detect nonclassicality and coherent errors in quantum circuits. This method efficiently classifies phase-coherent errors, even with noise, offering a new tool for quantum computing applications.

Keywords:
coherent errorspseudo-entropyquantum computingquantum error detectionquantum information

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Error Correction

Background:

  • Entanglement entropy quantifies quantum correlations but is limited to Hermitian operators.
  • Non-Hermitian systems and post-selection introduce complexities not captured by standard entropy.
  • Detecting and classifying coherent errors in quantum circuits is crucial for building fault-tolerant quantum computers.

Purpose of the Study:

  • To develop a simulation-based protocol for detecting nonclassicality and coherent errors in quantum circuits.
  • To utilize pseudo-entropy, specifically its imaginary part, as a diagnostic tool for quantum errors.
  • To establish theoretical benchmarks for classifying errors and inform hardware calibration.

Main Methods:

  • Definition and application of pseudo-entropy (Sˇ) as a complex-valued generalization of entanglement entropy.
  • Focus on the imaginary part of pseudo-entropy (ℑSˇ) for error diagnostics.
  • Simulation-based protocol involving threshold analysis to distinguish classical-like from quantum-like behavior.

Main Results:

  • The protocol enables resource-efficient classification of phase-coherent errors, including those from miscalibrated CNOT gates.
  • Demonstrated robustness to realistic noise conditions.
  • Numerical simulations show 55% of the parameter space classified as classical-like at hardware-calibrated sensitivity levels, with statistical significance.

Conclusions:

  • Pseudo-entropy provides a practical framework for identifying nonclassicality and classifying coherent errors in quantum circuits.
  • The imaginary part of pseudo-entropy serves as an effective diagnostic tool under realistic noise.
  • This work bridges theoretical concepts with practical applications in quantum error classification and hardware calibration.