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arXiv 2408.08786quant-ph
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相关错误对量子存储器的影响

Effect of Correlated Errors on Quantum Memory

Smita Bagewadi, Avhishek Chatterjee

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AI总结：

针对长程相关错误下量子存储器的容错问题，本文提出隐随机场推广的相关模型（含平稳遍历非马尔可夫分布），并基于非独立同分布测度集中性证明量子坦纳码在错误率低于阈值时可实现指数级保留时间，且相关性衰减速率不直接区分其优劣。

摘要：

近期关于基于LDPC码的恒定开销容错方案对抗独立同分布（i.i.d.）错误的研究成果，自然引出了针对长程相关错误的容错问题。理想情况下，任何相关性都可通过联合（系统与环境）哈密顿量描述，但任意联合哈密顿量通常难以处理，因此含成对项的联合哈密顿量模型在一系列基础工作中被提出并发展。然而，在该错误模型中分析新型恒定开销码极具挑战性。本文为建模量子存储器中的相关错误，引入一种作为著名隐随机场推广的相关模型，该模型包含平稳遍历（非马尔可夫）错误分布，能捕捉成对项联合哈密顿量模型无法捕捉的相关性。另一方面，基于非独立同分布测度集中性，我们证明：对于一大类非马尔可夫且（可能）非平稳的错误分布，当错误率低于阈值时，量子坦纳码（quantum Tanner codes）可确保指数级的保留时间（随物理量子比特数增长）。这些结果表明，相关性随距离的衰减速率不一定能区分“好”“坏”相关性。

英文摘要：

Recent results on constant overhead LDPC code-based fault-tolerance against i.i.d. errors naturally lead to the question of fault-tolerance against errors with long-range correlations. Ideally, any correlation can be captured by a joint (system and bath) Hamiltonian. However, an arbitrary joint Hamiltonian is often intractable, and hence, the joint Hamiltonian model with pairwise terms was introduced and developed in a series of foundational works. However, the analysis of the new constant overhead codes in that error model appears to be quite challenging. In this paper, to model correlated errors in quantum memory, we introduce a correlation model which is a generalization of the well-known hidden random fields. This proposed model, which includes stationary and ergodic (non-Markov) error distributions, is shown to capture correlations not captured by the joint Hamiltonian model with pairwise terms. On the other hand, building on non-i.i.d. measure concentration, we show that for a broad class of non-Markov and (possibly) non-stationary error distributions, quantum Tanner codes ensure an exponential retention time (in the number of physical qubits), when the error rate is below a threshold. An implication of these results is that the rate of decay of the correlation with distance does not necessarily differentiate between good and bad correlation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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