The k-local Pauli Commuting Hamiltonians Problem is in P
The k-local Pauli Commuting Hamiltonians Problem is in P
复制标题
k-局部泡利通勤哈密顿量问题位于 P
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Bacon
中科院分区：
文献类型：
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作者：
Jijiang Yan;D. Bacon
给定一个哈密顿量，它是可交换的少体项的和，可交换哈密顿量的问题是确定是否存在一个量子态，它是所有这些项的同时特征态，它使每一项都最小化。这个问题被认为是量子梅林-亚瑟复杂性类的问题，但人们普遍认为这类问题并不完整。在这里，我们证明了当单个项全部由泡利矩阵的张量积组成时，该问题的有限形式在经典计算机上有效地可解，因此在复杂度类p中，该问题可以被认为是辛向量空间上的经典XOR-SAT问题。这类问题包括基态具有拓扑纠缠的哈密顿量的实例，从而表明这种纠缠并不总是更一般问题的障碍。
Given a Hamiltonian that is a sum of commuting few-body terms, the commuting Hamiltonian problem is to determine if there exists a quantum state that is the simultaneous eigenstate of all of these terms that minimizes each term individually. This problem is known to be in the complexity class quantum Merlin-Arthur, but is widely thought to not be complete for this class. Here we show that a limited form of this problem when the individual terms are all made up of tensor products of Pauli matrices is efficiently solvable on a classical computer and thus in the complexity class P. The problem can be thought of as the classical XOR-SAT problem over a symplectic vector space. This class of problems includes instance Hamiltonians whose ground states possess topological entanglement, thus showing that such entanglement is not always a barrier for the more general problem.