匹配的有限表面码阈值的证明
Proof of finite surface code threshold for matching
摘要：
量子计算领域目前缺乏实验可行性的正式证明。量子比特是脆弱的，需要复杂的量子纠错来实现可靠的量子计算。表面码是一种很有前途的量子纠错码，它只需要一个物理上合理的具有最近邻相互作用的量子比特二维晶格。然而，现有的证据表明，使用这种代码进行可靠的量子计算是可能的，假设能够测量四体算符，尽管这一假设很难实现，但要求这些算符测量的误差率小于10^-9，这是一个非物理低目标。只有当假设强度和错误率的相互作用与距离无关时，高错误率才被证明是可以容忍的，这也是非物理的。在这项工作中，给定一个二维量子比特晶格，其中只有最近邻的两个量子比特门，以及单量子比特测量、初始化和幺正门，所有这些都具有错误率p，我们证明了在p<7.4x10^-4的情况下，任意可靠的量子计算是可能的，这是许多实验已经实现的目标。这解决了一个长期存在的开放问题，正式证明了在物理合理假设下量子计算的实验可行性。
英文摘要：
The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising quantum error correction code, requiring only a physically reasonable 2-D lattice of qubits with nearest neighbor interactions. However, existing proofs that reliable quantum computation is possible using this code assume the ability to measure four-body operators and, despite making this difficult to realize assumption, require that the error rate of these operator measurements is less than 10^-9, an unphysically low target. High error rates have been proved tolerable only when assuming tunable interactions of strength and error rate independent of distance, which is also unphysical. In this work, given a 2-D lattice of qubits with only nearest neighbor two-qubit gates, and single-qubit measurement, initialization, and unitary gates, all of which have error rate p, we prove that arbitrarily reliable quantum computation is possible provided p<7.4x10^-4, a target that many experiments have already achieved. This closes a long-standing open problem, formally proving the experimental feasibility of quantum computation under physically reasonable assumptions.
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