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The point of building a quantum computer is that it allows to model living things with predictive power and gives the opportunity to control life. Its scaling means not just the improvement of the instrument part, but also, mainly,…
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…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Quantum computers can solve specific problems that are not feasible on "classical" hardware. Harvesting the speed-up provided by quantum computers therefore has the potential to change any industry which uses computation, including finance.…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Quantum computing is a fascinating interdisciplinary research field that promises to revolutionize computing by efficiently solving previously intractable problems. Recent years have seen tremendous progress on both the experimental…
We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's…
This is an introductory review on the basic principles of quantum computation. Various important quantum logic gates and algorithms based on them are introduced. Quantum teleportation and decoherence are discussed briefly. Some problems,…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum…
Feynman's prescription for a quantum simulator was to find a hamitonian for a system that could serve as a computer. P\'olya and Hilbert conjecture was to demonstrate Riemann's hypothesis through the spectral decomposition of hermitian…
We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We…
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum…
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 implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…
This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…