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Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
After the emergence of quantum mechanics and realising its need for an accurate understanding of physical systems, numerical methods were being used to undergo quantum mechanical treatment. With increasing system correlations and size,…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
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…
Recent years have seen unprecedented advance in the design and control of quantum computers. Nonetheless, their applicability is still restricted and access remains expensive. Therefore, a substantial amount of quantum algorithms research…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
A quantum processor, like any computing device, requires the development of both hardware and the necessary set of software solutions, starting with quantum algorithms and ending with means of accessing quantum devices. As part of the…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
The paper is devoted to an approach to solving a problem of the efficiency of parallel computing. The theoretical basis of this approach is the concept of a $Q$-determinant. Any numerical algorithm has a $Q$-determinant. The $Q$-determinant…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
It is expected that quantum computers would enable solving various problems that are beyond the capabilities of the most powerful current supercomputers, which are based on classical technologies. In the last three decades, advances in…
Quantum neuromorphic computing physically implements neural networks in brain-inspired quantum hardware to speed up their computation. In this perspective article, we show that this emerging paradigm could make the best use of the existing…
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…