Quantum Error Correction in Adversarial Regimes

2025-09-10

AI Summary

In adversarial quantum environments, conventional quantum error correction tolerates at most ⌊d/2⌋ errors and yields a unique output, rendering it vulnerable to malicious tampering. To address this limitation, we propose a novel quantum list decoding framework. First, we generalize the Knill–Laflamme condition to characterize the class of quantum codes amenable to list decoding. Second, we design the first unambiguous list decoding protocol secure against polynomial-time quantum adversaries, supporting multi-round secure decoding. Our protocol integrates pseudorandom unitary operations with quantum cryptographic primitives, introducing computational-security guarantees against adversarial attacks. Crucially, it surpasses the fundamental ⌊d/2⌋ error-tolerance barrier of standard quantum error correction. This work establishes both a theoretical foundation and a practical pathway for robust quantum information processing in adversarial settings.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer. Quantum list decoding offers a promising alternative. By allowing the decoder to output a short list of possible errors, it becomes possible to tolerate far more errors, even under worst-case noise. But two fundamental questions remain: which quantum codes support list decoding, and can we design decoding schemes that are secure against efficient, computationally bounded adversaries? In this work, we answer both. To identify which codes are list-decodable, we provide a generalized version of the Knill-Laflamme conditions. Then, using tools from quantum cryptography, we build an unambiguous list decoding protocol based on pseudorandom unitaries. Our scheme is secure against any quantum polynomial-time adversary, even across multiple decoding attempts, in contrast to previous schemes. Our approach connects coding theory with complexity-based quantum cryptography, paving the way for secure quantum information processing in adversarial settings.

Problem

• Identifying which quantum codes support list decoding
• Designing decoding schemes secure against efficient adversaries
• Tolerating worst-case adversarial noise in quantum error correction

Innovation

• Generalized Knill-Laflamme conditions for list-decodable codes
• Pseudorandom unitaries enable unambiguous list decoding protocol
• Secure against quantum polynomial-time adversaries across multiple attempts