Simulating complex networks in phase space: Gaussian boson sampling
P. D. Drummond, Bogdan Opanchuk, A. Dellios, M. D. Reid
Abstract
We show how phase-space simulations of quantum states in a linear photonic network permit the verification of measurable probabilities and entanglement. We compare our predictions with recent Gaussian boson sampling experiments of Zhong et al. These use squeezed inputs and efficient ``on-off'' detectors, with up to 76th-order measured coincidence counts in the data. We introduce a general definition of grouped ``on-off'' detection probabilities for this purpose. The positive-$P$ phase-space method is used to compute any grouped or marginal click probabilities. Additional decoherence is included to obtain agreement between theory and experiment. The only limitation in estimating grouped probabilities is the computational sampling error, which is similar in magnitude to the experimental sampling error. The results obtained and graphed here are from first-order up to 16 000th-order grouped count probabilities. However, any order between these is also computable. We extend these results to include grouped probabilities with multidimensional outcomes that have a polynomial number of points. We also analyze quadrature detection experiments and show how to simulate genuine multipartite entanglement using Wigner phase-space methods.