Quantum circuits of c -- Z and SWAP gates optimization and entanglement

TL;DR

This paper explores the algebraic structure of quantum circuits with C-Z and SWAP gates to optimize their design and analyze how entanglement develops from initially unentangled states.

Contribution

It introduces an algebraic framework for these circuits, enabling optimization and deeper understanding of entanglement generation.

Findings

Optimized quantum circuits with C-Z and SWAP gates.

Insights into entanglement emergence from factorized states.

Algebraic characterization of circuit structures.

Abstract

We have studied the algebraic structure underlying the quantum circuits composed by $\cZ$ and $\Swap$ gates. Our results are applied to optimize the circuits and to understand the emergence of entanglement when a circuit acts on a fully factorized state.