Quantum Circuit Identities

TL;DR

This paper systematically constructs all quantum circuit identities involving up to three one-qubit operations, providing tools to simplify quantum circuits and reduce implementation costs.

Contribution

It presents a complete classification of small quantum circuit identities, aiding in circuit simplification and optimization.

Findings

All identities with 3 or fewer operations are explicitly constructed.

The identities can be used to reduce quantum circuit complexity.

Simplification leads to lower physical implementation costs.

Abstract

There are quantum circuit identities that simplify quantum circuits, reducing the effort needed physically to implement them. This paper constructs all identities made from 3 or fewer operations taken from a common set of one qubit operations, and explains how they may be used to simplify the cost of constructing quantum circuit identities.