Tensor Network Methods

Simone Montangero

Aaron C. Hoyt, Jonathan S. Bersson, Sean Garner +2 more

Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.

Yiwei Chen, K. Guo, Yilin Pan

The formalism of Tensor Network (TN) provides a compact way to approximate many-body quantum states with 1D chain of tensors. The 1D chain of tensors is found to be efficient in capturing the local correlations between neighboring subsystems, and machine learning approaches have been proposed using artificial neural networks (NN) of similar structure. However, a long chain of tensors is difficult to train due to exploding and vanishing gradients. In this paper, we propose methods to decompose the long-chain TN into short chains, which could improve the convergence property of the training algorithm by allowing stable stochastic gradient descent (SGD). In addition, the short-chain methods are robust to network initializations. Numerical experiments show that the short-chain TN achieves almost the same classification accuracy on MNIST dataset as LeNet-5 with less trainable network parameters and connections.

Thibaut Lacroix

Takumi Oshima, Yuma Ichikawa, Koji Hukushima

We propose a hybrid sampling method, tensor-network population annealing (TNPA), which combines tensor-network (TN) initialization with population annealing (PA). We apply this method to the two-dimensional Edwards-Anderson Ising spin glass. The approach is motivated by the limitations of existing methods: TN-based samplers can become numerically unstable in frustrated spin systems at low temperatures, whereas conventional PA requires a long annealing schedule when started from the high-temperature limit. In TNPA, TN contractions are used only within a reliable temperature range to generate initial configurations that are close to the equilibrium distribution. The subsequent low-temperature equilibration is then carried out by PA. To stabilize the initialization process, we introduce a diagnostic based on the effective sample size that adaptively selects the initialization temperature. The proposed framework provides a practical and physically motivated route to low-temperature sampling by combining the complementary strengths of TN and PA.

Joseph M. Landsberg