论文标题
Zak变换：Gottesman-Kitaev-Preskill代码的量子计算框架
The Zak transform: a framework for quantum computation with the Gottesman-Kitaev-Preskill code
论文作者
论文摘要
Gottesman-Kitaev-Preskill（GKP）代码使用周期性的波形编码量子量。此周期性使GKP代码成为Zak Transform的自然设置，该设置是量身定制的，可为周期性功能提供简单的描述。我们回顾了Zak的变换及其与希尔伯特空间中状态的Zak基础的联系，分解了支撑稳定器和可更正误差的移位操作员，并且我们发现位置波函数的Zak变换在GKP误差校正中自然而然地出现。我们通过将模式的Hilbert空间（以Zak为基础表示）划分为虚拟值和虚拟规模式的模式的希尔伯特空间（SSD）（模块化变量SSD）构建了新的骨值子系统分解（SSD）。在量规模式下进行跟踪具有逻辑质量状态，并且在特定逻辑规格相互作用之前，痕迹具有不同的逻辑状态 - 与GKP误差校正相关。
The Gottesman-Kitaev-Preskill (GKP) code encodes a qubit into a bosonic mode using periodic wavefunctions. This periodicity makes the GKP code a natural setting for the Zak transform, which is tailor-made to provide a simple description for periodic functions. We review the Zak transform and its connection to a Zak basis of states in Hilbert space, decompose the shift operators that underpin the stabilizers and the correctable errors, and we find that Zak transforms of the position wavefunction appear naturally in GKP error correction. We construct a new bosonic subsystem decomposition (SSD) -- the modular variable SSD -- by dividing a mode's Hilbert space, expressed in the Zak basis, into that of a virtual qubit and a virtual gauge mode. Tracing over the gauge mode gives a logical-qubit state, and preceding the trace with a particular logical-gauge interaction gives a different logical state -- that associated to GKP error correction.
