论文标题
通过同时对对角线化的Pauli集群对汉密尔顿模拟的电路优化
Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
论文作者
论文摘要
实际利益的许多应用都取决于汉密尔顿人的时间演变，这是由保利运营商总和给出的。单个保利操作员的精确时间演变的量子电路是众所周知的，可以通过连接单个术语的电路来微不足道地扩展到通勤的保利斯的总和。在本文中，我们通过将Pauli操作员分配为相互通勤群集并在应用同时对角线化后每个集群中的元素来降低了哈密顿模拟的电路复杂性。我们为将Paulis的分区集分配为通勤子集提供了一种实用算法，并表明所提出的方法可以有助于大大减少量子化学中汉密尔顿人的CNOT操作和电路深度的数量。同时对角线化的算法也适用于稳定剂状态的背景；特别是我们提供了新颖的四阶段和五阶段表示，每个表示仅包含一个条件门的一个阶段。
Many applications of practical interest rely on time evolution of Hamiltonians that are given by a sum of Pauli operators. Quantum circuits for exact time evolution of single Pauli operators are well known, and can be extended trivially to sums of commuting Paulis by concatenating the circuits of individual terms. In this paper we reduce the circuit complexity of Hamiltonian simulation by partitioning the Pauli operators into mutually commuting clusters and exponentiating the elements within each cluster after applying simultaneous diagonalization. We provide a practical algorithm for partitioning sets of Paulis into commuting subsets, and show that the proposed approach can help to significantly reduce both the number of CNOT operations and circuit depth for Hamiltonians arising in quantum chemistry. The algorithms for simultaneous diagonalization are also applicable in the context of stabilizer states; in particular we provide novel four- and five-stage representations, each containing only a single stage of conditional gates.
