arXiv 1702.005912017-02quant-ph

Lattice Surgery的优化是NP-Hard

Optimization of Lattice Surgery is NP-Hard

Daniel Herr, Franco Nori, Simon J. Devitt

发表信息：: npj Quantum Information 3, Article number: 35 (2017)
DOI：: 10.1038/s41534-017-0035-1

摘要：

在表面码或Raussendorf模型中的传统计算方法是在量子位的编码晶格内创建孔或“缺陷”，这些量子位通过拓扑编织来操纵以制定逻辑门。然而，这并不是实现通用容错计算的唯一方法。在这项工作中，我们专注于Lattice Surgery表示，它实现了横向逻辑运算，而不破坏固有的2D最近邻属性的编织为基础的表面码，并实现了通用性，没有缺陷和编织为基础的逻辑。对于这两种技术，存在关于量子线路的编译和资源优化的公开问题。辫子逻辑的优化被证明是困难的，与这个问题相关的经典复杂性尚未确定。在基于晶格手术的逻辑的上下文中，我们可以引入最优性条件，其对应于在物理量子位和计算时间方面具有最低资源需求的电路，并证明在晶格手术模型中优化量子线路的复杂性是NP-难的。

英文摘要：

The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates. However, this is not the only way to achieve universal, fault-tolerant computation. In this work, we focus on the Lattice Surgery representation, which realizes transversal logic operations without destroying the intrinsic 2D nearest-neighbor properties of the braid-based surface code and achieves universality without defects and braid based logic. For both techniques there are open questions regarding the compilation and resource optimization of quantum circuits. Optimization in braid-based logic is proving to be difficult and the classical complexity associated with this problem has yet to be determined. In the context of lattice-surgery-based logic, we can introduce an optimality condition, which corresponds to a circuit with the lowest resource requirements in terms of physical qubits and computational time, and prove that the complexity of optimizing a quantum circuit in the lattice surgery model is NP-hard.

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