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

• URL: http://arxiv.org/abs/2608.26241v1
• Date: Wed, 26 Aug 2026 18:00:00 GMT
• Title: Fast GHZ encoding with $1-o(1)$ fidelity
• Abstract summary: 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.<n>This saturates the theoretical lower bound $(log N/N)$, and by rescaling, also saturates the lower bound on signaling time for Hamiltonians with power-law interaction strengths $1/r$, $d$ in dimension $d$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $Ω(\log N/N)$, and by rescaling, also saturates the lower bound on signaling time for Hamiltonians with power-law interaction strengths $1/r^γ$, $γ<d$ in dimension $d$. The protocol uses spin-squeezing dynamics combined with quantum signal processing.

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