# Point Processes with Gaussian Boson Sampling

## TL;DR

This paper explores how Gaussian Boson Sampling, a quantum computing algorithm, can be used to generate complex point processes with clustering properties, offering new quantum-inspired statistical modeling tools.

## Contribution

It establishes a novel connection between quantum computing and point processes, introducing quantum-inspired models and a fast classical algorithm for permanental point processes.

## Key findings

- Gaussian Boson Sampling can implement intractable point processes.
- Point processes generated exhibit boson-like clustering.
- A new efficient classical algorithm for permanental point processes.

## 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.