论文标题
将振荡器的最佳编码用于更多振荡器
Optimal encoding of oscillators into more oscillators
论文作者
论文摘要
将量子信息编码为谐波振荡器是一种有效的噪声方法的方法。在这方面，振荡器到振荡器代码不仅在骨器编码中提供了额外的机会，而且还将误差校正的适用性扩展到量子传感和通信中无处不在的连续变量状态。在这项工作中，我们在Gottesman-Kitaev-Preskill（GKP）的一般家族中得出了最佳的振荡器到振荡器代码，用于均匀噪声。我们证明，任意GKP-Stabilizer代码可以简化为广义的GKP两种模式 - 平方（TMS）代码。最小化几何均值误差的最佳编码可以从具有优化的GKP晶格和TMS增益的GKP-TMS代码构建。对于单模数据和Ancilla，可以有效地解决此最佳代码设计问题，我们还提供了数值证据，表明六边形GKP晶格比以前采用的方格晶格是最佳且严格的。对于多模案例，一般的GKP晶格优化是具有挑战性的。在两种模式数据和Ancilla情况下，我们确定了D4晶格（一个4维密集的包装晶格），以优于较低尺寸晶格的产物。作为副产品，该代码减少使我们能够证明基于高斯编码的任意振荡器到振荡器的通用无阈值，即使Ancilla不是GKP状态。
Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also extend the applicability of error correction to continuous-variable states ubiquitous in quantum sensing and communication. In this work, we derive the optimal oscillator-to-oscillator codes among the general family of Gottesman-Kitaev-Preskill (GKP)-stablizer codes for homogeneous noise. We prove that an arbitrary GKP-stabilizer code can be reduced to a generalized GKP two-mode-squeezing (TMS) code. The optimal encoding to minimize the geometric mean error can be constructed from GKP-TMS codes with an optimized GKP lattice and TMS gains. For single-mode data and ancilla, this optimal code design problem can be efficiently solved, and we further provide numerical evidence that a hexagonal GKP lattice is optimal and strictly better than the previously adopted square lattice. For the multimode case, general GKP lattice optimization is challenging. In the two-mode data and ancilla case, we identify the D4 lattice -- a 4-dimensional dense-packing lattice -- to be superior to a product of lower dimensional lattices. As a by-product, the code reduction allows us to prove a universal no-threshold-theorem for arbitrary oscillators-to-oscillators codes based on Gaussian encoding, even when the ancilla are not GKP states.
