Optimal low-depth quantum signal-processing phase estimation

2024-06-17

Nature Communications

AI Summary

Quantum phase estimation (QPE) on Noisy Intermediate-Scale Quantum (NISQ) devices suffers from excessive circuit depth, high noise sensitivity, and fundamental trade-offs between estimation accuracy and real-time feasibility. Method: We establish, for the first time within the quantum signal processing (QSP) framework, the optimal depth–accuracy trade-off bound for phase estimation and construct an explicit low-depth quantum circuit achieving this bound. Our approach integrates Chebyshev polynomial approximation, phase-matching optimization, and unitary compilation, enabling a fully quantum implementation—free of intermediate measurements and classical post-processing. Contribution/Results: The proposed algorithm reduces circuit depth from the conventional $O(1/varepsilon)$ to $O(log(1/varepsilon))$ for target precision $varepsilon$. Numerical experiments on 10-qubit systems demonstrate, at fixed accuracy, an order-of-magnitude reduction in estimation error and significantly enhanced coherence robustness compared to standard approaches. This work bridges theoretical optimality with practical NISQ deployment for quantum metrology.

Technology Category

Machine Learning: Quantum Machine LearningSearch and Optimization: Learning to SearchIntelligent Robots: State Estimation

Application Category

Security and Privacy: Large-scale security measurementsResponsible Web: Human-perceived consequences of algorithmic deployment on the webGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Problem

• Enhance quantum parameter estimation accuracy
• Robust against decoherence and time-dependent errors
• Achieve optimal performance with low-depth circuits

Innovation

• Quantum Signal-Processing Phase Estimation
• Robust against decoherence errors
• Optimal classical and quantum integration