量子层码中的层码编码
Quantum Weight Reduction with Layer Codes
AI总结：
本文提出了一种简单通用的量子权重缩减方法，通过将Calderbank-Shor-Steane码替换为表面码补丁，实现低权重和低度数的层码，适用于模块化架构。
摘要：
量子权重缩减过程通过稀疏化量子码来简化其实现，从而得到低权重检查和低度数的量子比特。然而，迄今为止，只有少数量子权重缩减方法已被探索。在本文中，我们介绍了一种简单且通用的方法来实现量子权重缩减，该方法实现了检查权重为6和总量子比特度为6，这比现有方法的代价更低，但可能以更大的量子比特开销为代价。我们的量子权重缩减过程将任意Calderbank-Shor-Steane码中的每个量子比特和检查替换为一个丰富的表面码补丁，这些补丁随后被连接在一起，形成几何非局部的层码。这是简单经典权重缩减过程的量子类比，其中每个比特和检查被替换为重复码。由于我们权重缩减过程的简单性，所得到的码的权重和度数的界限直接来自层码构造，因此可以通过检查轻松验证。我们的方法适合在由表面码补丁通过长距离互连组成的模块化架构中实现。
英文摘要：
Quantum weight reduction procedures ease the implementation of quantum codes by sparsifying them, resulting in low-weight checks and low-degree qubits. However, to date, only few quantum weight reduction methods have been explored. In this work we introduce a simple and general procedure for quantum weight reduction that achieves check weight 6 and total qubit degree 6, lower than existing procedures at the cost of a potentially larger qubit overhead. Our quantum weight reduction procedure replaces each qubit and check in an arbitrary Calderbank-Shor-Steane code with an ample patch of surface code, these patches are then joined together to form a geometrically nonlocal Layer Code. This is a quantum analog of the simple classical weight reduction procedure where each bit and check is replaced by a repetition code. Due to the simplicity of our weight reduction procedure, bounds on the weight and degree of the resulting code follow directly from the Layer Code construction and hence are easily verified by inspection. Our procedure is well suited for implementation in modular architectures that consist of surface code patches networked via long-range interconnects.
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。
