Speedup in classical simulation of Gaussian boson sampling

Abstract

Gaussian boson sampling is a promising model for demonstrating quantum computational supremacy, which eases the experimental challenge of the standard boson-sampling proposal. Here by analyzing the computational costs of classical simulation of Gaussian boson sampling, we establish a lower bound for achieving quantum computational supremacy for a class of Gaussian boson-sampling problems, where squeezed states are injected into every input mode. Specifically, we propose a method for simplifying the brute-force calculations for the transition probabilities in Gaussian boson sampling, leading to a significant reduction of the simulation costs. Particularly, our numerical results indicate that we can simulate 18 photons Gaussian boson sampling at the output subspace on a normal laptop, 20 photons on a commercial workstation with 256 cores, and suggest about 30 photons for supercomputers. These numbers are significantly smaller than those in standard boson sampling, suggesting Gaussian boson sampling may be more feasible for demonstrating quantum computational supremacy.

The Walrus: a library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling

“…Our package has already been used in several research efforts to understand how to generate resource states for universal quantum computing (N. Tzitrin, Bourassa, Menicucci, & Sabapathy, 2019), study the dynamics of vibrational quanta in molecules (N Quesada, 2019;Valson Jacob, Kaur, Roga, & Takeoka, 2019), and develop the applications of GBS (Bromley et al, 2019) to molecular docking (Banchi, Fingerhuth, Babej, & Arrazola, 2019), graph theory (Schuld, Brádler, Israel, Su, & Gupt, 2019), and point processes (Jahangiri, Arrazola, Quesada, & Killoran, 2019). More importantly, it has been useful in delineating when quantum computation can be simulated by classical computing resources and when it cannot (Gupt, Arrazola, Quesada, & Bromley, 2018;Killoran et al, 2019;Nicolas Quesada & Arrazola, 2019;Wu, Cheng, Zhang, Yung, & Sun, 2019).…”

Benchmarking 50-Photon Gaussian Boson Sampling on the Sunway TaihuLight

“…To obtain a sample, it usually needs to calculate about 100 probabilities of the candidate samples using Markov [53], [54], [55], and [42], respectively.…”

Quadratic speedup for simulating Gaussian boson sampling

“…Two algorithms were also proposed in Ref. [28] for a restricted version of GBS. The first one has polynomial space complexity and O(poly(N )2 8N/3 ) time complexity; the second has exponential space complexity and O(poly(N )2 5N/2 ) time complexity.…”