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Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
An algebraic structure, Quotient Algebra Partition or QAP, is introduced in a serial of articles. The structure QAP is universal to Lie Algebras and enables algorithmic and exhaustive Cartan decompositions. The first episode draws the…
The encoding of classical to quantum data mapping through trigonometric functions within arithmetic-based quantum computation algorithms leads to the exploitation of multivariate distributions. The studied variational quantum gate learning…
The emergence of quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. The ability of quantum computers to scale computations implies better performance and…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…
In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
Advancements in Quantum Computing (QC) and Neural Combinatorial Optimization (NCO) represent promising steps in tackling complex computational challenges. On the one hand, Variational Quantum Algorithms such as QAOA can be used to solve a…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…
Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the…
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked…
Quipper is a recently released quantum programming language. In this report, we explore Quipper's programming framework by implementing the Deutsch's, Deutsch-Jozsa's, Simon's, Grover's, and Shor's factoring algorithms. It will help new…
A two-parameter quantum algebra $U_{qp}({\rm u}_2)$ is briefly investigated in this paper. The basic ingredients of a model based on the $U_{qp}({\rm u}_2)$ symmetry, the $qp$-rotator model, are presented in detail. Some general tendencies…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
This paper presents a Quantum Reinforcement Learning (QRL) solution to the dynamic portfolio optimization problem based on Variational Quantum Circuits. The implemented QRL approaches are quantum analogues of the classical…
An effective, accessible abstraction hierarchy has made using and programming computers possible for people across all disciplines. Establishing such a hierarchy for quantum programming is an outstanding challenge, especially due to a…
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
Recently, a quantum algorithm for a fundamentally important task in data mining, association rules mining (ARM), called qARM for short, has been proposed. Notably, qARM achieves significant speedup over its classical counterpart for…
With the applications of quantum computing becoming more and more widespread, finding ways that allow end users without experience in the field to apply quantum computers to solve their individual problems is becoming a crucial task.…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…