论文标题
稀疏图上量子多体物理的有效张量网络模拟
Efficient tensor network simulation of quantum many-body physics on sparse graphs
论文作者
论文摘要
我们研究了在稀疏连接的基础图上定义的张量网络状态。通用稀疏图是具有很高概率的扩张器图，并且只能用多项式资源有效地代表音量定律纠缠的状态。我们发现，通信推理算法（例如信仰传播）可以导致对稀疏图上定义的一类张量网络状态的局部期望值有效计算。作为应用，我们研究了平方根状态，图形状态的局部特性，并采用这种方法来制备在通用图上定义的大汉密尔顿人的基态。使用变分方法，我们研究了在稀疏扩展器图上定义的横向场量子源模型的相图。
We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial resources. We find that message-passing inference algorithms such as belief propagation can lead to efficient computation of local expectation values for a class of tensor network states defined on sparse graphs. As applications, we study local properties of square root states, graph states, and also employ this method to variationally prepare ground states of gapped Hamiltonians defined on generic graphs. Using the variational method we study the phase diagram of the transverse field quantum Ising model defined on sparse expander graphs.
