Classical Boson Sampling [R package BosonSampling version 0.1.3]

Changhun Oh, Minzhao Liu, Yuri Alexeev +2 more

Benoît Seron, Antoine Restivo

We present a free open source package for high performance simulation and numerical investigation of boson samplers and, more generally, multi-photon interferometry. Our package is written in Julia, allowing C-like performance with easy notations and fast, high-level coding. Underlying building blocks can easily be modified without complicated low-level language modifications. We present a great variety of routines for tasks related to boson sampling, such as statistical tools, optimization methods and classical samplers. Special emphasis is put on validation of experiments, where we present novel algorithms. This package goes beyond the boson sampling paradigm, allowing for the investigation of new interferometric behaviours such as bosonic bunching.

Claudio Conti

Timothy C. Ralph

We show that it is classically hard to sample the output distribution of certain continuous variable measurements from a BosonSampling device. Our argument is presented for exact BosonSampling. We discuss extending this result to approximate sampling.

P. H. Lundow, Klas Markström

In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we first discuss how to compute the permanent efficiently on a parallel computer, followed by algorithms which provide an exponential speed-up for sparse matrices and linear run times for matrices of limited bandwidth. The parallel algorithm has been implemented in a freely available software package, also available in an efficient serial version. As part of the timing runs for this package we set a new world record for the matrix order on which a permanent has been computed. Next we perform a simulation study of several conjectures regarding the distribution of the permanent for random matrices. Here we focus on permanent anti-concentration conjecture, which has been used to find the classical computational complexity of Boson sampling. We find a good agreement with the basic versions of these conjectures, and based on our data we propose refined versions of some of them. For small systems we also find noticeable deviations from a proposed strengthening of a bound for the number of photons in a Boson sampling system.

Rachel S. Chadwick