论文标题
费米量量子模拟的错误校正代码
Error-correcting codes for fermionic quantum simulation
论文作者
论文摘要
利用$ \ mathbb {z} _2 $ lattice量规理论的框架，在Pauli稳定器代码的背景下，我们提出了通过二维方形晶格通过Qubit System模拟费米的方法。我们研究了洛朗多项式环上保利模块的符合性自动形态。这使我们能够系统地增加稳定器代码的代码距离，同时固定编码的逻辑费米和物理速度之间的速率。我们确定适合费米亚模拟的稳定码的家族，达到$ d = 2,3,4,5,6,7 $的代码距离，允许对任何$ \ lfloor \ frac {d-1} {2} {2} \ rfloor $ qubit $ - Qubit $ - Qubit $ - Qubit-Qubit $ -QUBIT错误校正。与传统的代码串联方法相反，我们的方法可以增加代码距离而不会降低（费米子）代码速率。特别是，我们明确显示了所有稳定器和逻辑运算符的代码，其代码距离为$ d = 3,4,5 $。我们为所有Pauli错误提供综合征，并发明综合征匹配算法以数值计算代码距离。
Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of $d=2,3,4,5,6,7$, allowing correction of any $\lfloor \frac{d-1}{2} \rfloor$-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of $d=3,4,5$. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.
