Edge local complementation for logical cluster states

TL;DR

This paper introduces a method for implementing edge local complementation in graph states using Hadamard and CZ gates, enabling efficient construction of logical cluster states for quantum networks.

Contribution

It presents a novel approach to perform edge local complementation with minimal operations, facilitating scalable logical cluster state generation in quantum computing.

Findings

Efficient scheme for logical cluster state construction using edge local complementation.

Single physical CZ gate suffices for logical CZ operations between encoded qubits.

Potential for hierarchical quantum network development.

Abstract

A method is presented for the implementation of edge local complementation in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme to construct a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of edge local complementations. A single physical CZ operation, together with local operations, is sufficient to create a logical CZ operation between two logical qubits. The same construction can be used to generate any encoded graph state. This approach in concatenation may allow one to create a hierarchical quantum network for quantum information tasks.