Fast and Accurate GHZ Encoding Using All-to-all Interactions

• URL: http://arxiv.org/abs/2406.10336v1
• Date: Fri, 14 Jun 2024 18:00:02 GMT
• Title: Fast and Accurate GHZ Encoding Using All-to-all Interactions
• Authors: Chao Yin,
• Abstract summary: Greenberger-Horne-Zeilinger (GHZ) state is an important resource for quantum technologies. We consider the task of GHZ encoding using all-to-all interactions. We propose a fast protocol that achieves GHZ encoding with high accuracy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 and enhancing the rate of qubit 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.

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