Quantum circuits of CNOT gates

TL;DR

This paper explores the algebraic structure of CNOT-based quantum circuits, proposing optimization heuristics and algorithms to reduce gate count and generate entangled states efficiently.

Contribution

It introduces polynomial-time heuristics for CNOT circuit optimization and algorithms for creating entangled states from factorized states.

Findings

Proposed efficient heuristics for reducing CNOT gate count.

Developed algorithms for optimizing specific CNOT circuit cases.

Demonstrated methods to generate useful entangled states.

Abstract

We study in detail the algebraic structures underlying quantum circuits generated by CNOT gates. Our results allow us to propose polynomial-time heuristics to reduce the number of gates used in a given CNOT circuit and we also give algorithms to optimize this type of circuits in some particular cases. Finally we show how to create some usefull entangled states when a CNOT circuit acts on a fully factorized state.