Point processes with Gaussian boson sampling

Abstract

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of quantum computing to statistical modeling by establishing a connection between point processes and Gaussian Boson Sampling, an algorithm for special-purpose photonic quantum computers. We show that Gaussian Boson Sampling can be used to implement a class of point processes based on hard-to-compute matrix functions which, in general, are intractable to simulate classically. We also discuss situations where polynomial-time classical methods exist. This leads to a family of efficient quantum-inspired point processes, including a new fast classical algorithm for permanental point processes. We investigate the statistical properties of point processes based on Gaussian Boson Sampling and reveal their defining property: like bosons that bunch together, they generate collections of points that form clusters. Finally, we discuss several additional properties of these point processes which we illustrate with example applications.

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).…”

Exact simulation of Gaussian boson sampling in polynomial space and exponential time

“…The Gaussian state is typically obtained by sending squeezed light through a linear-optical interferometer, while more general versions employ displacements together with squeezing operations. GBS has raised additional interest due to the discovery of applications to quantum chemistry [13], optimization [14][15][16], graph similarity [17], and point processes [18]. Initial experimental implementations have also been recently reported [19][20][21].…”

Degenerate squeezing in waveguides: a unified theoretical approach

“…While part of this is due to fundamental interest, there are many practical applications of squeezed light as well, including computation [6], communication [7], and metrology [8]. In recent years, Gaussian Boson Sampling (GBS) [9,10] has emerged as one of the most actively researched applications [11][12][13][14][15][16][17][18].…”

“…We note that this situation is different from both the perturbative photon pair generation regime [26], as well as that of a continuous wave pump followed by homodyne detection [27]. Additionally, degenerate, rather than non-degenerate or so called twin-beam squeezing, is considered in studies of the hardness of GBS [9,10] and its applications [11][12][13][14][15][16][17][18].…”