Hopf algebra description of quantum circuits

TL;DR

This paper demonstrates that quantum circuits, specifically the controlled-NOT gate, can be modeled using Hopf algebra, enabling algebraic and unitary analysis of qubit operations.

Contribution

It introduces a Hopf algebra framework to describe and analyze quantum circuits, providing a new algebraic perspective on quantum computation.

Findings

Controlled-NOT gate described via Hopf algebra

Quantum circuits expressed as Hopf algebraic computations

Unified algebraic and unitary representation of qubit operations

Abstract

The controlled-NOT gate of qubit quantum circuits is shown to be described in terms of a Hopf algebra. Accordingly, any qubit quantum circuit can be expressed as the Hopf algebraic computations and unitary transformations on one qubit.