Approximate simulation of complex quantum circuits using sparse tensors

TL;DR

This paper introduces a novel method for approximately simulating complex quantum circuits using sparse tensor networks, enabling more efficient classical simulations of quantum systems.

Contribution

The authors develop a sparse tensor data structure and algorithms for efficient contraction and truncation, advancing quantum circuit simulation techniques.

Findings

Efficient contraction algorithms for sparse tensors.

Expected runtime scaling with qubit number and circuit depth.

Motivates future optimization research in sparse tensor networks.

Abstract

The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and software. Tensor networks have become forefront mathematical tools for these tasks. Here we introduce a method to approximately simulate quantum circuits using sparsely-populated tensors. We describe a sparse tensor data structure that can represent quantum states with no underlying symmetry, and outline algorithms to efficiently contract and truncate these tensors. We show that the data structure and contraction algorithm are efficient, leading to expected runtime scalings versus qubit number and circuit depth. Our results motivate future research in optimization of sparse tensor networks for quantum simulation.