Decoded Quantum Interferometry Under Noise

2025-08-14

AI Summary

This work investigates the robustness of Decoding Quantum Interferometry (DQI) under local depolarizing noise, aiming to elucidate how its quantum advantage persists in realistic noisy settings. Method: We introduce a noise-weighted sparsity parameter to construct a theoretical performance model for DQI and generalize Fourier spectral analysis to generic random Pauli noise. Leveraging quantum noise modeling, Fourier analysis, and large-scale numerical simulations, we validate our theory on canonical problems—including Max Linear/XOR-SAT and optimal polynomial intersection. Contribution/Results: Our framework precisely characterizes performance degradation under noise and reveals an exponential decay of solution quality with sparsity. Crucially, it extends beyond depolarizing noise to multiple noise models, providing a scalable theoretical toolkit and a new paradigm for designing noise-resilient quantum optimization algorithms.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Decoded Quantum Interferometry (DQI) is a recently proposed quantum optimization algorithm that exploits sparsity in the Fourier spectrum of objective functions, with the potential for exponential speedups over classical algorithms on suitably structured problems. While highly promising in idealized settings, its resilience to noise has until now been largely unexplored. To address this, we conduct a rigorous analysis of DQI under noise, focusing on local depolarizing noise. For the maximum linear satisfiability problem, we prove that, in the presence of noise, performance is governed by a noise-weighted sparsity parameter of the instance matrix, with solution quality decaying exponentially as sparsity decreases. We demonstrate this decay through numerical simulations on two special cases: the Optimal Polynomial Intersection problem and the Maximum XOR Satisfiability problem. The Fourier-analytic methods we develop can be readily adapted to other classes of random Pauli noise, making our framework applicable to a broad range of noisy quantum settings and offering guidance on preserving DQI's potential quantum advantage under realistic noise.

Problem

• Analyzes Decoded Quantum Interferometry resilience to local depolarizing noise
• Proves noise-weighted sparsity governs performance in maximum linear satisfiability
• Develops Fourier-analytic methods adaptable to other random Pauli noise

Innovation

• Decoded Quantum Interferometry exploits Fourier sparsity
• Analyzes DQI resilience under local depolarizing noise
• Fourier methods adapt to random Pauli noise