Remote controlled-NOT gate of d-dimension

TL;DR

This paper introduces a method to implement a remote controlled-NOT (CNOT) gate for qudits (d-dimensional quantum systems) using quantum teleportation, reducing resource consumption compared to traditional swap-based approaches.

Contribution

It extends the concept of remote CNOT gates from qubits to qudits, providing a resource-efficient method for quantum gate implementation in higher-dimensional systems.

Findings

Proposes a d-dimensional remote CNOT gate using entanglement and teleportation.

Identifies the role of quantum teleportation in remote quantum gate operations.

Reduces resource requirements compared to swap-based methods.

Abstract

Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we need a series of swap gates to transfer these two qubits to the nearest neighboring sites, and then after the CNOT gate we should transfer them to their original sites again. However, a series of swap gates are resource for quantum information processing. One economy way which does not consume so much resource is to implement CNOT gate remotely. The remote CNOT gate is to implement the CNOT gate for two remotely separated qubits with the help of one additional maximally entangled state. The original remote CNOT gate is for two qubits, here we will present the d-dimensional remote CNOT gate. The role of quantum teleportation is identified in the process of the remote CNOT gate.