Efficient quantum algorithms for $GHZ$ and $W$ states, and implementation on the IBM quantum computer

TL;DR

This paper introduces efficient algorithms for generating large entangled GHZ and W states, demonstrates their implementation on IBM quantum computers, and evaluates their quality and error correction prospects.

Contribution

It presents logarithmic complexity algorithms for entangled state generation and demonstrates their practical implementation on real quantum hardware up to 16 qubits.

Findings

Successful generation of GHZ and W states up to 16 qubits on IBM quantum computers.

Full quantum tomography confirms improved state quality for low-N states.

Quantum error correction schemes were found to be detrimental under current decoherence levels.

Abstract

We propose efficient algorithms with logarithmic step complexities for the generation of entangled $GHZ_N$ and $W_N$ states useful for quantum networks, and we demonstrate an implementation on the IBM quantum computer up to $N=16$. Improved quality is then investigated using full quantum tomography for low-$N$ GHZ and W states. This is completed by parity oscillations and histogram distance for large $N$ GHZ and W states respectively. We are capable to robustly build states with about twice the number of quantum bits which were previously achieved. Finally we attempt quantum error correction on GHZ using recent schemes proposed in the literature, but with the present amount of decoherence they prove detrimental.