论文标题
最佳本地统一编码电路的表面代码
Optimal local unitary encoding circuits for the surface code
论文作者
论文摘要
表面代码是由于其高阈值以及与现有实验架构的兼容性，是领先的候选量子纠正代码。 Bravyi等。 （2006年）表明，使用局部统一操作在表面代码中编码一个状态需要至少在晶格大小$ l $中线性的时间，但是Dennis等人引入的最有效的编码未知状态的已知方法。 （2002），具有$ O（l^2）$时复杂性。在这里，我们为平面表面代码提供了一个最佳的本地统一编码电路，该电路完全使用$ 2L $时间步长以在距离$ L $平面代码中编码未知状态。我们进一步展示了如何通过在$ o（\ log l）$ - 深度非本地重renormalisation编码器中执行loce locatity找到$ o（l）$复杂性的本地统一编码器。我们通过提供$ O（l）$本地统一电路来转换在复曲面代码和平面代码之间，并为矩形，旋转和3D表面代码提供最佳编码器来联系这些技术。此外，我们展示了如何使用平面代码的编码电路来制备紧凑型映射中的费米子状态，这是最近引入的Qubit映射的费米，其具有与表面代码相似的稳定器结构，并且特别有效地模拟费米 - 荷兰模型。
The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi et al. (2006) showed that encoding a state in the surface code using local unitary operations requires time at least linear in the lattice size $L$, however the most efficient known method for encoding an unknown state, introduced by Dennis et al. (2002), has $O(L^2)$ time complexity. Here, we present an optimal local unitary encoding circuit for the planar surface code that uses exactly $2L$ time steps to encode an unknown state in a distance $L$ planar code. We further show how an $O(L)$ complexity local unitary encoder for the toric code can be found by enforcing locality in the $O(\log L)$-depth non-local renormalisation encoder. We relate these techniques by providing an $O(L)$ local unitary circuit to convert between a toric code and a planar code, and also provide optimal encoders for the rectangular, rotated and 3D surface codes. Furthermore, we show how our encoding circuit for the planar code can be used to prepare fermionic states in the compact mapping, a recently introduced fermion to qubit mapping that has a stabiliser structure similar to that of the surface code and is particularly efficient for simulating the Fermi-Hubbard model.
