TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networks
This work provides a practical tool for researchers in quantum physics and computational science by implementing an efficient tensor network algorithm, though it is incremental as it applies existing methods to new hardware optimizations.
The authors tackled the problem of approximating ground states of quantum spin chains and lattice models using tree tensor networks, achieving computational speed-ups of up to 100 times when using GPUs compared to CPUs with bond dimensions ranging from 32 to 256.
TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice model on a thin torus (2D), and implement the algorithm using TensorNetwork. We use a standard energy minimization procedure over a TTN ansatz with bond dimension $χ$, with a computational cost that scales as $O(χ^4)$. Using bond dimension $χ\in [32,256]$ we compare the use of CPUs with GPUs and observe significant computational speed-ups, up to a factor of $100$, using a GPU and the TensorNetwork library.