Related papers: Quantum computing and polynomial equations over th…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…
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…
We use the benefits and components of classical computers every day. However, there are many types of problems which, as they grow in size, their computational complexity grows larger than classical computers will ever be able to solve.…
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…
The increasing growth of data volume, and the consequent explosion in demand for computational power, are affecting scientific computing, as shown by the rise of extreme data scientific workflows. As the need for computing power increases,…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
A quantum computer (QC) can solve many computational problems more efficiently than a classic one. The field of QCs is growing: companies (such as DWave, IBM, Google, and Microsoft) are building QC offerings. We position that software…
This research paper gives an overview of quantum computers - description of their operation, differences between quantum and silicon computers, major construction problems of a quantum computer and many other basic aspects. No special…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field…
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…
This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
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 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…
We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help…