对抗性噪声下的单次误差修正理论
A theory of single-shot error correction for adversarial noise
摘要：
单次误差校正是一种用于仅使用单轮噪声检查测量来校正物理误差的技术，使得任何残余噪声影响少量量子位。我们提出了一个一般理论的单次纠错，并建立了一个充分条件称为良好的健全的代码的测量检查。拓扑（或LDPC）码的良好的代码可靠性所示，需要相关的哈密顿量的宏观能垒。因此，带有局部校验的二维拓扑码不能具有良好的可靠性。在紧张局势与此同时，我们还表明，对于任何代码的测量检查的特定选择确实存在，提供良好的稳健性。换句话说，每个代码都可以执行单次纠错，但所需的检查可能是非本地的，并作用于许多量子位。如果我们希望代码具有良好的可靠性和简单的测量检查（LDPC属性），则需要仔细构造。最后，我们利用同调积的双重应用构造了具有单次纠错能力的量子LDPC码。我们的双同调乘积码通过一个我们称之为元检查的过程来利用测量检查中的冗余。
英文摘要：
Single-shot error correction is a technique for correcting physical errors using only a single round of noisy check measurements, such that any residual noise affects a small number of qubits. We propose a general theory of single-shot error correction and establish a sufficient condition called good soundness of the code's measurement checks. Good code soundness in topological (or LDPC) codes is shown to entail a macroscopic energy barrier for the associated Hamiltonian. Consequently, 2D topological codes with local checks can not have good soundness. In tension with this, we also show that for any code a specific choice of measurement checks does exist that provides good soundness. In other words, every code can perform single-shot error correction but the required checks may be nonlocal and act on many qubits. If we desire codes with both good soundness and simple measurement checks (the LDPC property) then careful constructions are needed. Finally, we use a double application of the homological product to construct quantum LDPC codes with single-shot error correcting capabilities. Our double homological product codes exploit redundancy in measurements checks through a process we call metachecking.
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