具有任意Z旋转逻辑门的量子码及其在容错码切换中的应用
Quantum Codes with Arbitrary Z-Rotation logical Gates and Applications to Fault-Tolerant Code Switching
中文总结 AI 辅助
本研究构建了支持任意Z旋转逻辑门的量子色码，扩展了容错码切换协议，实现了基于旋转表面码的低开销容错魔术态制备。
中文摘要 AI 辅助
实现通用容错量子操作集的一项技术是码切换方法，该方法利用两组具有互补横截门的量子码。迄今为止，该技术的应用在很大程度上仅限于支持逻辑T门的色码家族，对于许多其他重要家族（如旋转表面码）或更精细的Z旋转门，尚无类似的码切换协议。在本研究中，我们首先利用加倍技术作为统一框架，构建一类编码单个逻辑量子比特且最小距离任意大的量子色码，实现任意小逻辑Z旋转门的横截实现。我们研究该码族的结构特性，证明其在参数上优于最先进的三正交码，相比某些已知色码具有更低的量子比特开销，并且可通过元检查实现Z错码的单次解码。此外，我们表明该框架不仅适用于色码，具体而言，它可生成r正交量子码（r≥2），这些码继承了旋转表面码的局部几何结构。随后，我们提供一种开销优化协议以及若干候选码，专为在旋转表面码中实现逻辑Z旋转门而定制。最后，我们扩展基于横截CNOT门的容错码切换协议，以纳入Clifford层次任意层级下Z旋转门的容错实现，该协议适用于与旋转表面码兼容的几何结构。我们展示了首个通过码切换实现的容错魔术态制备演示，该演示采用距离为3的旋转表面码，仅使用总计45个物理量子比特，并通过模拟评估其性能。
英文摘要
A technique for realizing a universal set of fault-tolerant quantum operations is the code switching method, which leverages two quantum codes with complementary sets of transversal gates. To date, the application of this technique has been largely limited to families of color codes supporting a logical $T$ gate. No analogous code switching protocols exist for many other prominent families, such as rotated surface codes, or for finer $Z$-rotation gates. In this work, we first utilize the doubling technique as a unified framework to construct a class of quantum color codes encoding a single logical qubit with an arbitrarily large minimum distance, enabling the transversal realization of arbitrary small logical $Z$-rotation gates. We investigate the structural properties of this code family, demonstrating that they improve upon the parameters of state-of-the-art triorthogonal codes, achieve lower qubit overhead compared to certain known color codes, and admit single-shot decoding of $Z$-syndromes via meta-checks. Furthermore, we show that this framework extends beyond color codes; specifically, it enables the generation of $r$-orthogonal quantum codes, $r \ge 2$, that inherit the local geometry of rotated surface codes. We then provide an overhead optimization protocol alongside several candidate codes tailored for realizing logical $Z$-rotation gates within rotated surface codes. Finally, we extend the fault-tolerant code switching protocol based on transversal CNOT gates to incorporate fault-tolerant realization of $Z$-rotation gates at any level of the Clifford hierarchy for geometries compatible with rotated surface codes. We present the first demonstration of fault-tolerant magic state preparation by means of code switching within a distance-three rotated surface code using a total footprint of only 45 physical qubits, and evaluate its performance through a simulation.
