Fast GHZ encoding with $1-o(1)$ fidelity

Laura Shou; T. C. Mooney; Twesh Upadhyaya; Alexey V. Gorshkov

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arXiv · 2608.26241

Fast GHZ encoding with $1-o(1)$ fidelity

Laura Shou·T. C. Mooney·Twesh Upadhyaya·Alexey V. Gorshkov

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Abstract

We prove that $(1-o(1))$-fidelity $N$-qubit Greenberger--Horne--Zeilinger (GHZ) encoding can be performed in time $O(\log N/N)$ using all-to-all 2-local Hamiltonians with bounded 2-qubit interaction terms. This saturates the theoretical lower bound $\Omega(\log N/N)$, and by rescaling, also saturates the lower bound on signaling time for Hamiltonians with power-law interaction strengths $1/r^\gamma$, $\gamma<d$ in dimension $d$. The protocol uses spin-squeezing dynamics combined with quantum signal processing.

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Laura Shou, T. C. Mooney, Twesh Upadhyaya, Alexey V. Gorshkov. 2026-08-26. Fast GHZ encoding with $1-o(1)$ fidelity. https://arxiv.org/abs/2608.26241

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