论文标题
超快混合费用到Qubit映射
Ultrafast Hybrid Fermion-to-Qubit mapping
论文作者
论文摘要
费米映射在表示量子计算机上的费米子相互作用中起着至关重要的作用。有效的映射将系统的费尔米管模式转化为使用很少的辅助资源，以高度的位置进行Qubit相互作用。我们介绍了一个拥有当地的fermion to-Qubit映射家庭，其辅助量子比迄今为止已知的所有现有方案所需的尺寸较少。一个实例仅需要1.016 QUBITS-FERMION，而Y.-A的最著名的地方保留映射为1.25。 Chen和Y. Xu [Prx Quantum 4，010326（2023）]。我们的映射家庭（由Integer $ n $参数化）建立了辅助Qubits数量（$ \ frac {1} {n^2} $）与电路长度（$ o（\ log n）$）之间的直接权衡。此外，我们提出了一种非本地变体，该变体结合了约旦束缚和Bravyi-kitaev映射的强度，比Jordan-Wigner映射提供了98 \％的电路。这是通过在不同尺度上应用似乎不兼容的映射来实现的，这使他们各自的优势相互补充成为可能。
Fermion-to-qubit mappings play a crucial role in representing fermionic interactions on a quantum computer. Efficient mappings translate fermionic modes of a system to qubit interactions with a high degree of locality while using few auxiliary resources. We present a family of locality-preserving fermion-to-qubit mappings that require fewer auxiliary qubits than all existing schemes known to date. One instance requires only 1.016 qubits-per-fermion compared to 1.25 for the best-known locality-preserving mapping by Y.-A. Chen and Y. Xu [PRX Quantum 4, 010326 (2023)]. Our family of mappings (parameterised by integer $n$) establishes a direct trade-off between the number of auxiliary qubits ($\frac{1}{n^2}$) and the circuit length ($O(\log n)$). Furthermore, we present a non-local variant that combines the strengths of the Jordan-Wigner and Bravyi-Kitaev mappings to give 98\% shorter circuits than the Jordan-Wigner mapping. This is achieved by applying seemly incompatible mappings at different scales, making it possible for their respective strengths to complement each other.
