用于阿贝尔格点规范理论的二元高斯稳定子
Binary Gauss Stabilizers for Abelian Lattice Gauge Theories
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中文总结 AI 辅助
研究由\(\mathbb{Z}_{N}\)规范群描述的离散阿贝尔格点规范理论，找到二元高斯稳定子替代高斯算子，用于构建纠错码及规范固定，为格点规范理论及其量子模拟提供新工具，开辟交叉领域未来工作方向。
中文摘要 AI 辅助
规范理论和量子纠错码具有相同的底层结构：都利用约束来确定全希尔伯特空间的特定子空间。在量子纠错中，这些约束称为稳定子，在规范理论中对应高斯定律。本文考虑由\(\mathbb{Z}_{N}\)规范群描述的离散阿贝尔格点规范理论族，其中\(N\)是2的任意幂次。在此设定下，找到一组规范不变子空间的稳定子，即二元高斯稳定子，它是高斯算子的替代。利用该替代稳定子群构建实用的纠错码，无需额外量子比特。其应用不限于纠错，还提供了一种基于替代稳定子的规范固定新策略，可能优于轴规范等现有方法。结果为研究格点规范理论及其量子模拟提供了新工具，为格点规范理论与量子信息交叉领域的未来工作开辟了方向。
英文摘要
Gauge theories and quantum error-correcting codes share the same underlying structure: both use constraints to identify a specific subspace of the full Hilbert space. In quantum error correction, these constraints are known as stabilizers, while in gauge theories they correspond to Gauss law. In this work, we consider a family of discrete Abelian lattice gauge theories described by a $\mathbb{Z}_{N}$ gauge group with $N$ an arbitrary power of two. In this setting, we find a set of stabilizers for the gauge-invariant subspace which is an alternative to the Gauss operators, and we call them binary Gauss stabilizers. We use this alternative stabilizer group to build practical error-correcting codes exploiting the gauge symmetries of the system without the addition of extra qubits. The applications of our finding are not limited to error correction though. We also provide a new strategy of gauge fixing to remove the redundancies based on our alternative stabilizer, which might provide advantages with respect to already-existing approaches such as the axial gauge. Our results provide new tools to study lattice gauge theories and their quantum simulation, and opens directions for future work at the interface of lattice gauge theory and quantum information.
