论文标题
6季度最佳克利福德电路
6-qubit Optimal Clifford Circuits
论文作者
论文摘要
Clifford组位于量子计算的核心 - 它是量子误差校正的基础，其元素可用于执行魔术状态蒸馏，并形成随机基准测试协议，Clifford组用于研究量子纠缠等等。实践中利用Clifford组元素的能力在很大程度上取决于其电路级实施的效率。寻找短路是一个棘手的问题。尽管Clifford Group是有限的，但其尺寸随Qubits $ n $的数量而迅速增长，将已知的最佳实现限制为$ n {=} 4 $ Qubits。对于$ n {=} 6 $，Clifford组元素的数量约为$ 2.1 {\ cdot} 10^{23} $。在本文中，我们报告了一组算法以及它们的C/C ++实现，通过将后者的一个子集存储在大小为2.1TB的数据库中（1KB = 1024b），它们通过将后者的子集存储在所有6 Quition Clifford组元素中隐含地合成了最佳电路。我们演示了如何使用消费者和企业级计算机（硬件）分别提取$ 0.0009358 $和$ 0.0006274 $秒的任意最佳6 Qubit Clifford电路，同时依靠此数据库。
Clifford group lies at the core of quantum computation -- it underlies quantum error correction, its elements can be used to perform magic state distillation and they form randomized benchmarking protocols, Clifford group is used to study quantum entanglement, and more. The ability to utilize Clifford group elements in practice relies heavily on the efficiency of their circuit-level implementation. Finding short circuits is a hard problem; despite Clifford group being finite, its size grows quickly with the number of qubits $n$, limiting known optimal implementations to $n{=}4$ qubits. For $n{=}6$, the number of Clifford group elements is about $2.1{\cdot}10^{23}$. In this paper, we report a set of algorithms, along with their C/C++ implementation, that implicitly synthesize optimal circuits for all 6-qubit Clifford group elements by storing a subset of the latter in a database of size 2.1TB (1KB=1024B). We demonstrate how to extract arbitrary optimal 6-qubit Clifford circuit in $0.0009358$ and $0.0006274$ seconds using consumer- and enterprise-grade computers (hardware) respectively, while relying on this database.
