# Optimized contraction scheme for tensor-network states

## TL;DR

This paper introduces an optimized contraction scheme for tensor-network states that significantly reduces computational costs, enabling the study of larger bond dimensions and expanding the applicability of tensor-network methods.

## Contribution

The authors propose mapping double-layer tensor networks onto intersected single-layer networks, greatly improving efficiency and accuracy in evaluating tensor-network states.

## Key findings

- Almost doubles the maximum bond dimension for reliable calculations
- Reduces local tensor bond dimensions, improving efficiency
- Extends the scope of tensor-network applications

## Abstract

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of carrying out this contraction is generally very high, which limits the largest bond dimension of tensor-network states that can be accurately studied to a relatively small value. We propose an optimized contraction scheme to solve this problem by mapping the double-layer tensor network onto an intersected single-layer tensor network. This reduces greatly the bond dimensions of local tensors to be contracted and improves dramatically the efficiency and accuracy of the evaluation of expectation values of tensor-network states. It almost doubles the largest bond dimension of tensor-network states whose physical properties can be efficiently and reliably calculated, and it extends significantly the application scope of tensor-network methods.