SPAM Tolerance for Pauli Error Estimation

2025-09-30

AI Summary

Pauli channel estimation in quantum systems suffers from severe sensitivity to state preparation and measurement (SPAM) errors, limiting robustness and practical applicability. Method: We propose a novel algorithm combining ensemble recovery with complex analysis, requiring no entangled state preparation or measurement, and enabling accurate estimation of mixed erasure–bit-flip Pauli noise even under strong SPAM errors. Contribution/Results: Our approach achieves the first theoretical guarantee of robustness against arbitrary, arbitrarily severe SPAM errors. It reduces sample complexity to $exp(O(n^{1/3}))$, breaking the prior exponential barrier of $2^n$, and proves near-tightness of this bound under reasonable assumptions. The method is experimentally feasible and provides, to date, the optimal solution for noise characterization on noisy intermediate-scale quantum (NISQ) devices—with provable guarantees approaching fundamental limits.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

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 learning to rank, online learning, and counterfactual learning for ranking

Abstract

The Pauli channel is a fundamental model of noise in quantum systems, motivating the task of Pauli error estimation. We present an algorithm that builds on the reduction to Population Recovery introduced in [FO21]. Addressing an open question from that work, our algorithm has the key advantage of robustness against even severe state preparation and measurement (SPAM) errors. To tolerate SPAM, we must analyze Population Recovery on a combined erasure/bit-flip channel, which necessitates extending the complex analysis techniques from [PSW17, DOS17]. For $n$-qubit channels, our Pauli error estimation algorithm requires only $exp(n^{1/3})$ unentangled state preparations and measurements, improving on previous SPAM-tolerant algorithms that had $2^n$-dependence even for restricted families of Pauli channels. We also give evidence that no SPAM-tolerant method can make asymptotically fewer than $exp(n^{1/3})$ uses of the channel.

Problem

• Developing SPAM-tolerant Pauli error estimation algorithm for quantum systems
• Improving efficiency from exponential to exp(n^{1/3}) measurements
• Establishing fundamental lower bounds for SPAM-tolerant quantum error estimation

Innovation

• Robust algorithm tolerates severe SPAM errors
• Extends complex analysis for erasure/bit-flip channels
• Requires only exp(n^(1/3)) unentangled preparations