We provide a theoretical framework for encoding arbitrary logical states of a quantum bit (qubit) into a continuous-variable quantum mode through quantum walks. Starting with a squeezed vacuum state of the quantum mode, we show that quantum walks of the state in phase space can generate output states that are variants of codeword states originally put forward by Gottesman, Kitaev and Preskill (GKP) (Phys Rev A 64:012310, 2001). In particular, with a coin-toss transformation that projects the quantum coin onto the diagonal coin state, we show that the resulting dissipative quantum walks can generate qubit encoding akin to the prototypical GKP encoding. We analyze the performance of these codewords for error corrections and find that even without optimization our codewords outperform the GKP ones by a narrow margin. Using the circuit representation, we provide a general architecture for the implementation of this encoding scheme and discuss its possible realization through circuit quantum-electrodynamics systems.

中文翻译：

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通过相空间中的量子游走将qubit编码为谐波振荡器模式

我们提供了一个理论框架，用于通过量子游走将量子位（qubit）的任意逻辑状态编码为连续变量量子模式。从量子模式的压缩真空状态开始，我们证明了相空间中状态的量子游走可以生成输出状态，这些输出状态是Gottesman，Kitaev和Preskill（GKP）最初提出的码字状态的变体（Phys Rev A 64： 012310，2001）。特别是，通过将量子硬币投射到对角硬币状态的硬币抛物转换，我们证明了产生的耗散性量子游走可以生成类似于原型GKP编码的qubit编码。我们分析了这些码字的纠错性能，发现即使不进行优化，我们的码字也要比GKP字窄得多。使用电路表示，我们提供了用于实现此编码方案的通用体系结构，并讨论了通过电路量子电动力学系统可能实现的编码方案。