Related papers: Point Processes with Gaussian Boson Sampling
A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…
The difficulty of validating large-scale quantum devices, such as Boson Samplers, poses a major challenge for any research program that aims to show quantum advantages over classical hardware. To address this problem, we propose a novel…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
A growing cohort of experimental linear photonic networks implementing Gaussian boson sampling (GBS) have now claimed quantum advantage. However, many open questions remain on how to effectively verify these experimental results, as…
Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…
Boson-sampling is a simplified model for quantum computing that may hold the key to implementing the first ever post-classical quantum computer. Boson-sampling is a non-universal quantum computer that is significantly more straightforward…
Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly,…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
This thesis is based upon the work I have done during my PhD candidature at Macquarie University. In this work we develop quantum technologies that are directed towards realising a quantum computer. Specifically, we have made many…
In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…
Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
Quantum computing aims at exploiting quantum phenomena to efficiently perform computations that are unfeasible even for the most powerful classical supercomputers. Among the promising technological approaches, photonic quantum computing…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…