Quantum circuit optimization for unitary operators over non-adjacent qudits

TL;DR

This paper presents a general strategy for optimizing quantum circuits by representing quantum gates as block matrices for qubits and qudits in arbitrary positions, with applications in quantum computational logic.

Contribution

It introduces a novel method for representing and optimizing quantum gates over non-adjacent qubits and extends this approach to qudits, enhancing quantum circuit design flexibility.

Findings

Effective block-matrix representation for non-adjacent qubits

Extension of the model to qudits

Application in quantum computational logic

Abstract

Within the general context of the architecture in quantum computer design, this paper aims is to provide a general strategy to obtain a block-matrix representation of quantum gates applied to qubits placed in arbitrary positions over an arbitrary dimensional input state. The model is also extended to the framework of quantum computation with qudits. An application in the context of the quantum computational logic is provided.