Nonclassicality and Coherent Error Detection via Pseudo-Entropy

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.