Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908300298158080 |
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| author | Yin, Chao |
| author_facet | Yin, Chao |
| contents | 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 $Ω(\log N/N)$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_10336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions Yin, Chao Quantum Physics 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 $Ω(\log N/N)$. 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. |
| title | Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.10336 |