Effective simulation of state distribution in qubit chains

TL;DR

This paper presents a method for simulating quantum state distribution in qubit chains using a specific set of quantum gates related to Spin groups, enabling classical modeling of processes like state transfer and quantum walks.

Contribution

It introduces a classical simulation approach for quantum state distribution in qubit chains based on non-universal gate sets linked to Spin groups, connecting to matchgates and quantum complexity.

Findings

Classical simulation of quantum state transfer is feasible with this approach.

The method models various quantum walks effectively.

It relates quantum gates to Spin groups and matchgates.

Abstract

This work recollects a non-universal set of quantum gates described by higher-dimensional Spin groups. They are also directly related with matchgates in theory of quantum computations and complexity. Various processes of quantum state distribution along a chain such as perfect state transfer and different types of quantum walks can be effectively modeled on classical computer using such approach.