Log-depth entanglement transition in hypercube Gaussian boson sampling

Abstract:We study an entanglement transition at logarithmic depth in random hypercube linear optical networks. Starting from an initial Gaussian state with all modes squeezed, we prove that random hypercube linear optical networks on $n$ modes generate ensemble-averaged subsystem entanglement within a constant factor of its maximum in all subsystems at circuit depth $\Theta(\log n)$. Below depth $\log_2n$, there is an extensive subsystem with no entanglement. The entanglement generation in logarithmic depth can be compared to recent progress towards $O(\log n)$ depth average-case sampling hardness for Gaussian boson sampling in a hypercube network.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR)

arXiv:2609.12043 [quant-ph]

(or arXiv:2609.12043v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.12043 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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