Although stoquastic Hamiltonians are known to be simulable via sign-problem-free quantum Monte Carlo (QMC) techniques, the nonstoquasticity of a Hamiltonian does not necessarily imply the existence of a QMC sign problem. We give a sufficient and necessary condition for the QMC-simulability of Hamiltonians in a given basis: We prove that a QMC simulation will be sign-problem-free if and only if all the overall total phases along the chordless cycles of the weighted graph whose adjacency matrix is the Hamiltonian are zero (modulo $2\pi$). We use our findings to provide a construction for nonstoquastic, yet sign-problem-free and hence QMC-simulable, quantum many-body models. We also demonstrate why the simulation of truly sign-problematic models using the QMC weights of the stoquasticized Hamiltonian is generally suboptimal. We offer a superior alternative.

中文翻译：

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确定具有几何相位的量子蒙特卡洛可模拟性

尽管已知可以通过无符号问题的量子蒙特卡洛（QMC）技术来模拟随机哈密顿量，但是哈密顿量的非随机性并不一定意味着存在QMC符号问题。我们在给定的基础上为哈密顿量的QMC可模拟性提供了充分必要的条件：我们证明，当且仅当沿着加权图的无弦周期的所有总总相位的QMC模拟将无符号问题时，QMC模拟才会无符号问题。邻接矩阵是哈密顿量为零（模$\mathrm{2个}\pi$）。我们使用我们的发现为非随机的，但无符号问题的构造提供了构造，因此也可以进行QMC模拟的量子多体模型。我们还证明了为什么使用随机化的哈密顿量的QMC权重对真正的符号问题模型进行模拟通常不是最佳的。我们提供了一个更好的选择。