论文标题
量子振幅阻尼代码的线性编程边界
Linear programming bounds for quantum amplitude damping codes
论文作者
论文摘要
鉴于近似量子误差（AQEC）代码的性能比完美的量子误差校正代码具有更好的性能，因此量化其性能是相关的。虽然量子重量枚举者在量子误差校正代码的最小距离上建立了一些最佳的上限，但这些边界并不直接应用于AQEC代码。本文中，我们引入了量子重量枚举器，以进行振幅阻尼（AD）误差（AD）误差，并在近似量子误差校正的框架内工作。特别是，我们介绍了一个辅助精确的枚举器，该枚举枚举机构是代码空间的固有的，此外，我们在量子重量枚举方枚举AD错误与此辅助精确的权重枚举之间建立了线性关系。这使我们能够建立一个线性程序，仅当不存在具有相应参数的AQEC AD代码时，该程序才是不可行的。为了说明我们的线性程序，我们从数值上排除了能够纠正任意AD错误的三量Qubit AD代码的存在。
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds do not directly apply to AQEC codes. Herein, we introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. In particular, we introduce an auxiliary exact weight enumerator that is intrinsic to a code space and moreover, we establish a linear relationship between the quantum weight enumerators for AD errors and this auxiliary exact weight enumerator. This allows us to establish a linear program that is infeasible only when AQEC AD codes with corresponding parameters do not exist. To illustrate our linear program, we numerically rule out the existence of three-qubit AD codes that are capable of correcting an arbitrary AD error.
