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摘要翻译：
本文分析了量子计算机在相关环境下运行量子纠错码(QEC)时的长时间行为。从实际噪声模型的哈密顿公式出发，假设QEC确实是可能的，我们得到了编码在约化密度矩阵中的故障路径概率和剩余退相干的形式表达式。对于门时间为非零的系统（“长门”），我们用噪声的一个上界进行了分析。为了引入一个量子比特的局部错误概率，我们假设信号在环境中的传播慢于QEC周期（超立方体假设）。这允许在广义自旋玻色子模型和量子挫折模型的情况下进行显式计算。关键结果是一个维度判据：如果关联衰减得足够快，系统就会向随机误差模型演化，容错量子计算的门限定理已经证明了这一点。另一方面，如果相关性衰减较慢，这个阈值定理的传统证明就不成立了。这个维度准则与量子相变理论中的准则有许多相似之处。
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英文标题：
《Hamiltonian Formulation of Quantum Error Correction and Correlated
Noise: The Effects Of Syndrome Extraction in the Long Time Limit》
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作者：
E. Novais, Eduardo R. Mucciolo, Harold U. Baranger
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Quantum Physics 量子物理学
分类描述：Description coming soon
描述即将到来
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Computer Science 计算机科学
二级分类：Information Theory 信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Mathematics 数学
二级分类：Information Theory 信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
We analyze the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a faulty path and the residual decoherence encoded in the reduced density matrix. Systems with non-zero gate times (``long gates'') are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of signals through the environment is slower than the QEC period (hypercube assumption). This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions.
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PDF链接：
https://arxiv.org/pdf/710.1624
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