Minimization of Quantum Circuits using Quantum Operator Forms

TL;DR

This paper introduces the Quantum Operator Form (QOF), a new representation for quantum circuits that enables efficient minimization using a variety of quantum gates beyond traditional methods.

Contribution

It presents the QOF as a novel quantum circuit representation and provides minimization rules and a pseudo-algorithm for optimizing circuits with CNOT, CV, and CV^ gates.

Findings

QOF allows circuit minimization with multiple quantum gate types.

The proposed rules enable exact circuit realizations.

Demonstrates improved circuit optimization techniques.

Abstract

In this paper we present a method for minimizing reversible quantum circuits using the Quantum Operator Form (QOF); a new representation of quantum circuit and of quantum-realized reversible circuits based on the CNOT, CV and CV$^\dagger$ quantum gates. The proposed form is a quantum extension to the well known Reed-Muller but unlike the Reed-Muller form, the QOF allows the usage of different quantum gates. Therefore QOF permits minimization of quantum circuits by using properties of different gates than only the multi-control Toffoli gates. We introduce a set of minimization rules and a pseudo-algorithm that can be used to design circuits with the CNOT, CV and CV$^\dagger$ quantum gates. We show how the QOF can be used to minimize reversible quantum circuits and how the rules allow to obtain exact realizations using the above mentioned quantum gates.