Related papers: Algorithmic Perspective on Toda's Theorem
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
Recent improvement on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and…
The aim of this work is to show a brand-new way of making deterministic Quantum Computing (short QC), in the sense of Theory of Calculability, by meaning of unitary evolution. We start from the original Shor's Algorithm to explain how the…
The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep learning, most prominently its lack of trustworthiness, may…
Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
A new implementation of an adiabatically-trained ensemble model is derived that shows significant improvements over classical methods. In particular, empirical results of this new algorithm show that it offers not just higher performance,…
The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that…
We study the effects of approximate inference on the performance of Thompson sampling in the $k$-armed bandit problems. Thompson sampling is a successful algorithm for online decision-making but requires posterior inference, which often…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Quantum query complexity is known to be characterized by the so-called quantum adversary bound. While this result has been proved in the standard discrete-time model of quantum computation, it also holds for continuous-time (or…
Database theory is exciting because it studies highly general and practically useful abstractions. Conjunctive query (CQ) evaluation is a prime example: it simultaneously generalizes graph pattern matching, constraint satisfaction, and…
We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models…
Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics.…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…