# Point processes with Gaussian boson sampling.

@article{Jahangiri2020PointPW, title={Point processes with Gaussian boson sampling.}, author={Soran Jahangiri and Juan Miguel Arrazola and Nicol{\'a}s Quesada and Nathan Killoran}, journal={Physical review. E}, year={2020}, volume={101 2-1}, pages={ 022134 } }

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 photonic quantum computers. We show that Gaussian boson sampling can be used to implement a class of point processes…

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## References

SHOWING 1-10 OF 76 REFERENCES

Gaussian boson sampling using threshold detectors

- Computer SciencePhysical Review A
- 2018

It is proved that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, the model remains intractable to simulate classically under standard complexity-theoretic conjectures.

Detailed study of Gaussian boson sampling

- Computer Science, PhysicsPhysical Review A
- 2019

An expression is derived that relates the probability to measure a specific photon output pattern from a Gaussian state to the Hafnian matrix function and is used to design aGaussian Boson sampling protocol.

Some properties of point processes in statistical optics

- Physics
- 2010

The analysis of the statistical properties of the point process (PP) of photon detection times can be used to determine whether or not an optical field is classical, in the sense that its statistical…

Using Gaussian Boson Sampling to Find Dense Subgraphs.

- MathematicsPhysical review letters
- 2018

Focusing on the NP-hard densest k-subgraph problem, it is found that stochastic algorithms are enhanced through GBS, which selects dense subgraphs with high probability, based on a link between graph density and the number of perfect matchings-enumerated by the Hafnian.

Noninteracting fermions in a trap and random matrix theory

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

We review recent advances in the theory of trapped fermions using techniques borrowed from random matrix theory (RMT) and, more generally, from the theory of determinantal point processes. In the…

THE COINCIDENCE APPROACH TO STOCHASTIC POINT PROCESSES

- Mathematics
- 1975

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to…

Quantum approximate optimization with Gaussian boson sampling

- Computer SciencePhysical Review A
- 2018

This work shows that Gaussian boson sampling (GBS) can be used to enhance any stochastic algorithm for this NP-Hard problem called Max-Haf and confirms that all algorithms are improved when employing GBS, and that GBS-enhanced random search performs the best despite being the one with the simplest underlying classical routine.

Distributions on Partitions, Point Processes,¶ and the Hypergeometric Kernel

- Mathematics
- 1999

Abstract:We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove…

Free Fermions and the Classical Compact Groups

- MathematicsJournal of statistical physics
- 2018

A finite temperature extension of the Haar measure on the classical compact groups and the eigenvalue statistics of the resulting grand canonical matrix models corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.

What can quantum optics say about complexity theory?

- Computer SciencePhysical review letters
- 2015

Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, a general formula is derived for calculating the output probabilities, and by considering input thermal states, it is shown that theoutput probabilities are proportional to permanents of positive-semidefinite Hermitian matrices.