具有证明距离和低权重测量的高编码率量子码
High-Rate Quantum Codes with Proven Distance and Low-Weight Measurements
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中文总结 AI 辅助
本研究提出一族任意维矩形网格上的量子子系统码，证明其dressed距离，并在10,000数据量子比特预算下给出距离16、32、64时编码率与测量权重的权衡，最高保护4,096个逻辑量子比特。
中文摘要 AI 辅助
我们研究了一族定义在任意维矩形坐标网格上的量子子系统码，其边长均为偶数且至少为4。直接测量的算符沿坐标线作用。对于该族中的每个码，我们推导出受保护逻辑量子比特的数量，并在无需数值搜索的情况下证明其dressed距离。为说明由此产生的设计选择，我们设定数据量子比特数不超过10,000的预算，并确定该族在距离16、32和64下编码率与测量权重之间的完整权衡关系。在距离16时，一个码使用权重为10的测量，在10,000个数据量子比特中保护4,096个逻辑量子比特。在距离32和64时，分别使用7,776和9,216个数据量子比特的码，通过权重为6的测量，保护1,024和256个逻辑量子比特。我们在论文中穿插并解释了Lean代码片段，以引导读者完成对子系统码构造及其dressed和bare距离的形式化验证。
英文摘要
We study a family of quantum subsystem codes defined on rectangular coordinate grids of any dimension, with even side lengths of at least four. The directly measured operators act along coordinate lines. For every member of the family, we derive the number of protected logical qubits and prove its dressed distance without a numerical search. To illustrate the resulting design choices, we impose a budget of at most 10,000 data qubits and determine the complete tradeoff between encoding rate and measurement weight within this family at distances 16, 32, and 64. At distance 16, one code protects 4,096 logical qubits among 10,000 data qubits using weight-ten measurements. At distances 32 and 64, codes with 7,776 and 9,216 data qubits protect 1,024 and 256 logical qubits, respectively, using weight-six measurements. We include and explain Lean code snippets throughout the paper to guide readers through the formal verification of our subsystem-code construction and its dressed and bare distances.
发表机构
- Joint Center for Quantum Information and Computer Science (QuICS)（量子信息与计算机科学联合中心）
- University of Maryland, College Park（马里兰大学帕克分校）
- Technology Innovation Institute（技术创新研究所）
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