Floquet Majorana XYZ 码及其可调逻辑动力学
Floquet Majorana XYZ Codes with Tunable Logical Dynamics
- Institute for Advanced Study, Tsinghua University（清华大学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
我们基于 Majorana XYZ 子系统码构造 Floquet 码，通过测量循环调度实现逻辑量子比特在静态与动态形式间的切换，并首次同时实现局域量子比特表示与微观 Majorana 实现。
AI中文摘要：
我们从 Majorana XYZ 子系统码出发构造 Floquet 码，该码在量子比特中以及直接在微观 Majorana 模式中均具有局域实现，晶格大小为 $L\ imes L$。对于三步循环，奇数 $L$ 支持一个静态逻辑量子比特，而偶数 $L$ 支持两个。对于 $L=4n+2$ 的偶数 $L$，两个逻辑量子比特均具有与时间无关的 Pauli 代表元。相比之下，对于 $L=4n$，第二个逻辑量子比特的一个 Pauli 算符在整个循环中保持不变，而其共轭的每个代表元则必须随测量循环演化。这一区别源于依赖于奇偶性的代数障碍，当循环缩减为两步时该障碍消失，从而恢复完全静态的逻辑对。因此，通过测量调度，同一编码逻辑自由度可在静态与部分动态形式之间切换。在具有一个开放方向的情况下，可仅使用局域 Majorana 奇偶性测量来实现合适的协议。据我们所知，这是首个同时具有局域量子比特表示和直接微观 Majorana 实现的 Floquet 码族。
英文摘要：
We construct Floquet codes from the Majorana XYZ subsystem code with local realizations both in qubits and directly in microscopic Majorana modes with lattice size $L\times L$. For a three-step cycle, odd $L$ supports one static logical qubit, whereas even $L$ supports two. For even $L$ with $L=4n+2$, both logical qubits admit time-independent Pauli representatives. For $L=4n$, by contrast, one Pauli of the second logical qubit remains fixed throughout the cycle, while every representative of its conjugate must evolve through the measurement cycle. This distinction follows from a parity-dependent algebraic obstruction and disappears when the cycle is reduced to two steps, which restores a fully static logical pair. Thus, the same encoded logical degree of freedom can be switched between static and partially dynamical forms by the measurement schedule. With one open direction, suitable protocols can be implemented using only local Majorana parity measurements. To our knowledge, this is the first Floquet-code family with both a local qubit representation and a direct microscopic Majorana realization.
