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

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.