论文标题
同时进行的
Simultaneous Stoquasticity
论文作者
论文摘要
混血的汉密尔顿人在当地哈密顿问题的计算复杂性以及经典的模拟性研究中发挥了作用。特别是，可以使用蒙特卡洛技术直接模拟了混乱的哈密顿量。我们解决了一个问题，即是否可以通过统一的转变同时使两个或更多的汉密尔顿人同时进行。这个问题对模拟量子退火的复杂性具有重要意义，而量子优势与涉及退化的汉密尔顿人的静止性有关。我们发现，对于几乎所有问题，没有这样的统一存在，并表明确定这种单一的存在的问题等同于确定在初始和转化的汉密尔顿人的基质元素中是否有解决多项式（IN）平等系统的解决方案。解决这样的方程系统是NP-HARD。我们从广义Bloch向量的集合来强调对该问题的几何理解。
Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.
