基于Z₂格点规范理论高斯定律的任意距离量子纠错码
Arbitrary-Distance Quantum Error Correction with Gauss's Law for $\mathbb Z_2$ Lattice Gauge Theory
AI总结：
本研究将基于Z₂格点规范理论高斯定律的量子纠错码推广至任意t量子比特错误，推导最优码并对比验证其在降低编码哈密顿量局域性及t≤3时减少物理量子比特开销的优势。
AI中文摘要：
Rajput、Roggero和Wiebe此前已证明，Z₂高斯定律约束可用于构建对任意单量子比特错误具有鲁棒性的高效量子纠错码（QECC）。本研究将该构造推广为对任意t量子比特错误（t为任意正整数）具有鲁棒性，其中包含通过最小化给定码距所需的物理量子比特数，推导所考虑族内的最优高斯定律码。最后，在码容量设置下，从物理量子比特数、编码哈密顿量的局域性及逻辑错误率等指标，将本研究的码与其他高效QECC对比。与对每个格点自由度使用领域无关的码相比，发现高斯定律码的主要优势在于降低编码哈密顿量的局域性；此外，当t≤3（码距d≤7）时，物理量子比特开销也有所降低。
英文摘要：
It has previously been shown by Rajput, Roggero, and Wiebe that $\mathbb Z_2$ Gauss's law constraints can be used to build efficient quantum error-correcting codes (QECCs) that are robust against arbitrary single-qubit errors. In this work, we generalize the construction to be robust against arbitrary $t$-qubit errors, where $t$ is any positive integer. This includes a derivation of the optimal Gauss's law code within the considered family by minimizing the number of physical qubits required for a given code distance. Finally, we compare our codes against other efficient QECCs on metrics such as the number of physical qubits, the locality of the encoded Hamiltonian, and the logical error rate in the code capacity setting. Compared to using a domain-agnostic code for every lattice degree of freedom, we find that the Gauss's law code primarily excels at reducing the locality of the encoded Hamiltonian. Moreover, the physical qubit overhead is also reduced for $t \le 3$ (distance $d \le 7$).
