Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions

TL;DR

This paper introduces a rapid, high-fidelity protocol for GHZ state encoding in quantum systems using all-to-all interactions, significantly improving speed and accuracy over naive methods, with potential applications in quantum error correction and information transmission.

Contribution

The authors develop a fast GHZ encoding protocol utilizing all-to-all interactions that approaches the theoretical speed limit and achieves high fidelity for large system sizes.

Findings

Encoding time scales as O(log^2 N / N), close to the theoretical limit.

Final state fidelity exceeds 99.9% for system sizes up to 2000 qubits.

Uses data qubit as control with spin-squeezing dynamics for efficient encoding.

Abstract

The $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state is an important resource for quantum technologies. We consider the task of GHZ encoding using all-to-all interactions, which prepares the GHZ state in a special case, and is furthermore useful for quantum error correction, interaction-rate enhancement, and transmitting information using power-law interactions. The naive protocol based on parallelizing CNOT gates takes $\mathrm{O}(1)$-time of Hamiltonian evolution. In this work, we propose a fast protocol that achieves GHZ encoding with high accuracy. The evolution time $\mathrm{O}(\log^2N/N)$ almost saturates the theoretical limit $\Omega(\log N/N)$. Moreover, the final state is close to the ideal encoded one with high fidelity $> 1-10^{-3}$, up to large system sizes $N\lesssim 2000$. The protocol only requires a few stages of time-independent Hamiltonian evolution; the key idea is to use the data qubit as control, and to use fast spin-squeezing dynamics generated by e.g. two-axis-twisting.