论文标题
在两个空间维度中的费米映射之间的等效性
Equivalence between fermion-to-qubit mappings in two spatial dimensions
论文作者
论文摘要
我们认为，可以通过参考文献中的确切持续化来生成二维晶格上费米子观测值和保利矩阵之间的所有保存量的映射。 [1]，其规格约束项目以繁殖费米为基础的子空间。从确切的效率化并应用Clifford有限深度的局部统一（GLU）转换开始，我们可以实现所有可能的费米式映射（直到重新划分Majorana fermions）。特别是，我们在平方晶格上使用每个费用1.25量列表发现了一种新的超级冲洗编码，该编码比文献中的任何方法都低。我们证明存在具有Qubit-Fermion比率$ r = 1+ \ frac {1} {2k} $的费米对量映射，用于正整数$ k $，在两个空间尺寸中，证明利用了量子量细胞automata（qca）的琐事。当比率接近1时，费米亚与Qubit的映射将沿二维晶格中的某个路径降低至1D Jordan-Wigner转换。最后，我们明确地证明了Bravyi-Kitaev超快速模拟，Verstraete-Cirac辅助方法，Kitaev的精确解决的模型，Majorana Loop稳定器代码以及紧凑型费疗法映射均可从确切的效率化中获得。
We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization in Ref. [1], whose gauge constraints project onto the subspace of the toric code with emergent fermions. Starting from the exact bosonization and applying Clifford finite-depth generalized local unitary (gLU) transformation, we can achieve all possible fermion-to-qubit mappings (up to the re-pairing of Majorana fermions). In particular, we discover a new super-compact encoding using 1.25 qubits per fermion on the square lattice, which is lower than any method in the literature. We prove the existence of fermion-to-qubit mappings with qubit-fermion ratios $r=1+ \frac{1}{2k}$ for positive integers $k$, where the proof utilizes the trivialness of quantum cellular automata (QCA) in two spatial dimensions. When the ratio approaches 1, the fermion-to-qubit mapping reduces to the 1d Jordan-Wigner transformation along a certain path in the two-dimensional lattice. Finally, we explicitly demonstrate that the Bravyi-Kitaev superfast simulation, the Verstraete-Cirac auxiliary method, Kitaev's exactly solved model, the Majorana loop stabilizer codes, and the compact fermion-to-qubit mapping can all be obtained from the exact bosonization.
