论文标题
量子量规网络：一种新型的张量网络
Quantum Gauge Networks: A New Kind of Tensor Network
论文作者
论文摘要
尽管张量网络是模拟低维量子物理学的强大工具，但在较高的空间维度下，张量网络算法在计算上的昂贵。我们介绍了量子量规网络：另一种张量网络ANSATZ，对于较大的空间维度而言，模拟的计算成本不会明确增加。我们从量子动力学的量规图中汲取灵感，该图像由每个空间斑块的局部波函数组成，并带有与单一连接相关的相邻斑块。量子量规网络（QGN）具有相似的结构，除了局部波形和连接的希尔伯特空间尺寸被截断。我们描述了如何从通用波函数或矩阵乘积状态（MPS）获得QGN。 $ m $的所有波函数的所有$ 2K $ - 点相关功能，许多运算符都可以通过具有债券尺寸$ o（m^k）$的QGN编码。相比之下，只需$ k = 1 $，$ 2^{m/6} $的指数较大的债券尺寸通常是MPS Qubits所需的。我们提供了一种简单的QGN算法，用于在任何空间维度中对量子动力学的近似模拟。近似动力学可以实现与时间无关的汉密尔顿人的精确节能，并且还可以准确地保持空间对称性。我们通过在多达三个空间维度中模拟费米子哈密顿量的量子淬火来基准测试算法。
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of tensor network ansatz for which the computation cost of simulations does not explicitly increase for larger spatial dimensions. We take inspiration from the gauge picture of quantum dynamics, which consists of a local wavefunction for each patch of space, with neighboring patches related by unitary connections. A quantum gauge network (QGN) has a similar structure, except the Hilbert space dimensions of the local wavefunctions and connections are truncated. We describe how a QGN can be obtained from a generic wavefunction or matrix product state (MPS). All $2k$-point correlation functions of any wavefunction for $M$ many operators can be encoded exactly by a QGN with bond dimension $O(M^k)$. In comparison, for just $k=1$, an exponentially larger bond dimension of $2^{M/6}$ is generically required for an MPS of qubits. We provide a simple QGN algorithm for approximate simulations of quantum dynamics in any spatial dimension. The approximate dynamics can achieve exact energy conservation for time-independent Hamiltonians, and spatial symmetries can also be maintained exactly. We benchmark the algorithm by simulating the quantum quench of fermionic Hamiltonians in up to three spatial dimensions.
