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Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…
A theoretical model of a quantum device which can factorize any number N in two steps i.e. by preparing an input state and performing a measurement is discussed. The analysis reveals that the duration of state preparation and measurement is…
In previous works, we showed that an optimal quantum algorithm can always be seen as a sum over classical histories in each of which the problem solver knows in advance one of the possible halves of the solution she will read in the future…
In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the…
Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
The identification of causal relations is a cornerstone of the scientific method. Traditional approaches to this task are based on classical statistics. However, such classical approaches do not apply in the quantum domain, where a broader…
We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
Proposed quantum advantage in electronic structure has so far required significant fine-tuning to find problems where classical heuristics fail. We describe how to obtain robust quantum speedups for correlated electronic structure and…
Quantum computers have the potential to solve certain problems faster than classical computers by exploiting quantum mechanical effects such as superposition. However, building high-quality quantum software is challenging due to the…
A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are…
The ability to identify cause-effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…