Simulating quantum circuits using tree tensor networks

TL;DR

This paper introduces a classical simulation method for quantum circuits using tree tensor networks, optimizing for entanglement structure to improve efficiency over traditional matrix product states.

Contribution

It presents a novel algorithm that adapts tree tensor network structures to simulate quantum circuits more efficiently, with theoretical analysis and numerical validation.

Findings

Efficient simulation of quantum circuits up to 37 qubits

Identification of scenarios where tree tensor networks outperform matrix product states

Analysis of computational cost and memory requirements

Abstract

We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected entanglement generated by the quantum circuit. The gates are sequentially applied to the tree by absorbing single-qubit gates into leaf nodes, and splitting two-qubit gates via singular value decomposition and threading the resulting virtual bond through the tree. We theoretically analyze the applicability of the method as well as its computational cost and memory requirements, and identify advantageous scenarios in terms of required bond dimensions as compared to a matrix product state representation. The study is complemented by numerical experiments for different quantum circuit layouts up to 37 qubits.