Log-depth entanglement transition in hypercube Gaussian boson sampling

• URL: http://arxiv.org/abs/2609.12043v1
• Date: Thu, 10 Sep 2026 18:00:00 GMT
• Title: Log-depth entanglement transition in hypercube Gaussian boson sampling
• Abstract summary: We study an entanglement transition at logarithmic depth in random hypercube linear optical networks.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $Θ(\log n)$. 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.

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