Efficient simulation of parametrized quantum circuits under non-unital noise through Pauli backpropagation

2025-01-22

AI Summary

Efficient classical simulation of parameterized quantum circuits under non-unitary noise—such as amplitude damping—on NISQ devices remains a fundamental challenge. Method: This work extends the Pauli backpropagation technique to model general non-unitary quantum channels and introduces a combinatorial complexity framework with rigorous analytical guarantees. Contribution/Results: We prove that the algorithm retains polynomial time complexity even under realistic hardware noise models, substantially extending the applicability beyond conventional unitary-only simulators. Experimental evaluation demonstrates high accuracy and scalability on variational quantum circuits subject to amplitude damping noise. To our knowledge, this is the first classical benchmarking tool for near-term quantum advantage verification that simultaneously ensures theoretical rigor and practical utility. It significantly enhances the reliability and interpretability of quantum–classical performance comparisons in noisy regimes.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

As quantum devices continue to grow in size but remain affected by noise, it is crucial to determine when and how they can outperform classical computers on practical tasks. A central piece in this effort is to develop the most efficient classical simulation algorithms possible. Among the most promising approaches are Pauli backpropagation algorithms, which have already demonstrated their ability to efficiently simulate certain classes of parameterized quantum circuits-a leading contender for near-term quantum advantage-under random circuit assumptions and depolarizing noise. However, their efficiency was not previously established for more realistic non-unital noise models, such as amplitude damping, that better capture noise on existing hardware. Here, we close this gap by adapting Pauli backpropagation to non-unital noise, proving that it remains efficient even under these more challenging conditions. Our proof leverages a refined combinatorial analysis to handle the complexities introduced by non-unital channels, thus strengthening Pauli backpropagation as a powerful tool for simulating near-term quantum devices.

Problem

• Quantum Circuit Simulation
• Parameterized Quantum Circuits
• Quantum Advantage

Innovation

• Pauli Backpropagation Algorithm
• Complex Noise Simulation
• Parameterized Quantum Circuits