量子规范网络：一种新型张量网络
Quantum Gauge Networks: A New Kind of Tensor Network
AI总结：
本文提出量子规范网络（QGN），一种计算成本不随空间维度显式增长的新型张量网络，并给出从一般波函数或MPS构造QGN的方法及适用于任意空间维度的量子动力学近似模拟算法。
摘要：
尽管张量网络是模拟低维量子物理的强大工具，但在更高空间维度中，张量网络算法的计算代价非常高。我们引入量子规范网络：一种不同类型的张量网络拟设，其模拟计算成本不会随着空间维度的增大而显式增加。我们从量子动力学的规范图景中获得启发，该图景由每个空间补丁的局域波函数组成，相邻补丁通过酉连接相关联。量子规范网络（QGN）具有类似的结构，只是局域波函数和连接的希尔伯特空间维度被截断。我们描述了如何从一般波函数或矩阵乘积态（MPS）获得QGN。对于M个算符，任意波函数的所有$2k$点关联函数都可以由键维度为$O(M^k)$的QGN精确编码。相比之下，仅对于$k=1$，量子比特的MPS通常需要指数级更大的键维度$2^{M/6}$。我们提供了一个简单的QGN算法，用于在任意空间维度中对量子动力学进行近似模拟。该近似动力学可以对时间无关哈密顿量实现精确能量守恒，并且空间对称性也可以被精确保持。我们通过模拟最多三个空间维度中的费米子哈密顿量的量子淬火来对该算法进行基准测试。
英文摘要：
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.
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