arXiv:2609.12043v1 Announce Type: new 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.
Log-depth entanglement transition in hypercube Gaussian boson sampling
arXiv:2609.12043v1 Announce Type: new 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 entangle...