EinExprs: Contraction Paths of Tensor Networks as Symbolic Expressions

TL;DR

EinExprs.jl is a Julia package that optimizes tensor network contraction paths using symbolic expressions, offering advanced algorithms and benchmarks on quantum circuit simulations.

Contribution

Introduces a symbolic expression-based representation for tensor network contraction paths and provides a Julia package with multiple optimization methods.

Findings

State-of-the-art contraction path optimization achieved.

Effective methods demonstrated on random quantum circuit simulations.

Benchmark results show improved efficiency over existing approaches.

Abstract

Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path optimization that offers state-of-art optimizers. We propose a representation of the contraction path of a Tensor Network based on symbolic expressions. Using this package the user may choose among a collection of different methods such as Greedy algorithms, or an approach based on the hypergraph partitioning problem. We benchmark this library with examples obtained from the simulation of Random Quantum Circuits (RQC), a well known example where Tensor Networks provide state-of-the-art methods.