Recent advancements in multi-mode Gottesman-Kitaev-Preskill (GKP) codes have shown great promise in enhancing the protection of both discrete and analog quantum information. This broadened range of protection brings opportunities beyond quantum computing to benefit quantum sensing by safeguarding squeezing — the essential resource in many quantum metrology protocols. However, the potential for quantum sensing to benefit quantum error correction has been less explored. In this work, we provide a unique example where techniques from quantum sensing can be applied to improve multi-mode GKP codes. Inspired by distributed quantum sensing, we propose the distributed two-mode squeezing (dtms) GKP codes that offer benefits in error correction with minimal active encoding operations. Indeed, the proposed codes rely on a $single$ (active) two-mode squeezing element and an array of beamsplitters that effectively distributes continuous-variable correlations to many GKP ancillae, similar to continuous-variable distributed quantum sensing. Despite this simple construction, the code distance achievable with dtms-GKP qubit codes is comparable to previous results obtained through brute-force numerical search [19]. Moreover, these codes enable analog noise suppression beyond that of the best-known two-mode codes [11] without requiring an additional squeezer. We also provide a simple two-stage decoder for the proposed codes, which appears near-optimal for the case of two modes and permits analytical evaluation.

中文翻译：

---

通过分布式两模式压缩保护振荡器和 Qudits


多模式 Gottesman-Kitaev-Preskill (GKP) 码的最新进展在增强离散和模拟量子信息的保护方面显示出了巨大的前景。这种扩大的保护范围带来了超越量子计算的机会，通过保护挤压（许多量子计量协议中的重要资源）来使量子传感受益。然而，量子传感有益于量子纠错的潜力却很少被探索。在这项工作中，我们提供了一个独特的示例，其中可以应用量子传感技术来改进多模式 GKP 代码。受分布式量子传感的启发，我们提出了分布式双模式压缩 (dtms) GKP 代码，该代码通过最少的主动编码操作提供纠错优势。事实上，所提出的代码依赖于单个（有源）双模式挤压元件和分束器阵列，可有效地将连续变量相关性分布到许多 GKP 辅助装置，类似于连续变量分布式量子传感。尽管结构简单，但使用 dtms-GKP 量子位代码可实现的代码距离与之前通过强力数值搜索获得的结果相当[19]。此外，这些代码能够实现超越最著名的双模式代码 [11] 的模拟噪声抑制，而无需额外的压缩器。我们还为所提出的代码提供了一个简单的两级解码器，它对于两种模式的情况看起来接近最佳，并且允许分析评估。