Related papers: Remarks on the nature of quantum computation
Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers. However, today's quantum computers still have limited demonstrable functionality, and it is expected that scaling up to…
We present a class of hybrid classical systems using quantum co-processors and point out that unlike purely quantum computers, such hybrids can be both universal and Turing complete; we introduce such quantum-classical hybrids as…
Developing a systematic view of where quantum computers will outperform classical ones is important for researchers, policy makers and business leaders. But developing such a view is challenging because quantum advantage analyses depend not…
We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
In this paper, we consider three types of polynomial equations in quantum computer: linear divisibility equation, which belongs to a special type of binary-quadratic Diophantine equation; quadratic congruence equation with restriction in…
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…
Quantum computation provides exponential speedup for solving certain mathematical problems against classical computers. Motivated by current rapid experimental progress on quantum computing devices, various models of quantum computation…
Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
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…
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…
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…
The quantum multicomputer consists of a large number of small nodes and a qubus interconnect for creating entangled state between the nodes. The primary metric chosen is the performance of such a system on Shor's algorithm for factoring…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Numerous reports claim that quantum advantage, which should emerge as a direct consequence of the advent of quantum computers, will herald a new era of chemical research because it will enable scientists to perform the kinds of quantum…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
Quantum computers can in principle solve certain problems exponentially more quickly than their classical counterparts. We have not yet reached the advent of useful quantum computation, but when we do, it will affect nearly all scientific…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…