Abstract
We introduce an exact classical algorithm for simulating Gaussian Boson Sampling (GBS). The complexity of the algorithm is exponential in the number of photons detected, which is itself a random variable. For a fixed number of modes, the complexity is in fact equivalent to that of calculating output probabilities, up to constant prefactors. The simulation algorithm can be extended to other models such as GBS with threshold detectors, GBS with displacements, and sampling linear combinations of Gaussian states. In the specific case of encoding non-negative matrices into a GBS device, our method leads to an approximate sampling algorithm with polynomial runtime. We implement the algorithm, making the code publicly available as part of Xanadu's The Walrus library, and benchmark its performance on GBS with random Haar interferometers and with encoded Erd\H{o}s-Renyi graphs.
Highlights
Boson sampling is a model of photonic quantum computing that was introduced to argue that that nonuniversal photonic quantum computers cannot be efficiently simulated classically [1]
For every B there is a corresponding setting of interferometer and squeezing parameters [43]. We simulate this setting for a Gaussian boson sampling (GBS) device with m = 100 modes and an interferometer unitary chosen at random from the Haar measure
We have described an exact classical algorithm for simulating GBS
Summary
Boson sampling is a model of photonic quantum computing that was introduced to argue that that nonuniversal photonic quantum computers cannot be efficiently simulated classically [1]. [25], extending these techniques to GBS has been challenging because these algorithms rely on specific properties of boson sampling that are not present in GBS Despite these challenges, an exact simulation algorithm has been reported and implemented for the specific case of GBS with threshold detectors [26,27]. An exact simulation algorithm has been reported and implemented for the specific case of GBS with threshold detectors [26,27] This algorithm suffers from the critical drawback that its memory requirement scales exponentially, limiting the scope of problems that can be simulated. The method presented here can be applied to several other models, including GBS with threshold detectors, GBS with displacements, and sampling linear combinations of Gaussian states. The code used to generate these results is freely available as part of Xanadu’s The Walrus library [28]
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