相关论文: There, and Back Again: Quantum Theory and Global O…

The complexity of large-scale 6G-and-beyond networks demands innovative approaches for multi-objective optimization over vast search spaces, a task often intractable. Quantum computing (QC) emerges as a promising technology for efficient…

In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear…

In a recent paper [2], Chang et al. have proposed studying "Quantum $\mathbb{F}_{un}$": the $q \mapsto 1$ limit of Modal Quantum Theories over finite fields $\mathbb{F}_q$, motivated by the fact that such limit theories can be naturally…

The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…

We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…

Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…

Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…

Quantum key distribution (QKD) systems require optimal performance of both quantum and classical channels - utilizing as few as possible qubits and bits for establishing as many as possible key bits. Here we report a way to determine if a…

Quantum optimisation is emerging as a promising approach alongside classical heuristics and specialised hardware, yet its performance is often difficult to assess fairly. Traditional benchmarking methods, rooted in digital complexity…

We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…

The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm…

Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…

A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…

In this study, we propose a global optimization algorithm based on quantizing the energy level of an objective function in an NP-hard problem. According to the white noise hypothesis for a quantization error with a dense and uniform…

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of…

This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…