Related papers: Mathematical Foundations of Quantum Computing for …
Quantum state manipulation of two-qubits on the local systems by special unitaries induces special orthogonal rotations on the Bloch spheres. An exact formula is given for determining the local unitaries for some given rotation on the Bloch…
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…
This is a short introduction to Quantum Computing intended for physicists. The basic idea of a quantum computer is introduced. Then we concentrate on Shor's integer factoring algorithm.
An architecture for a quantum computer is presented in which spins associated with donors in silicon function as qubits. Quantum operations on the spins are performed using a combination of voltages applied to gates adjacent to the spins…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
This paper considers two frequently used matrix representations -- what we call the $\chi$- and $\mathcal{S}$-matrices -- of a quantum operation and their applications. The matrices defined with respect to an arbitrary operator basis, that…
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
In this article, we present an introduction to quantum computing (QC) tailored for computing professionals such as programmers, machine learning engineers, and data scientists. Our approach abstracts away the physics underlying QC, which…
The first prototypes of quantum computers sparked interest in quantum computing and the basic principles of quantum mechanics. The education project on the physical bases of quantum computing is part of this context, based on the…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
The aim of the present paper is twofold. First, to give the main ideas behind quantum computingand quantum information, a field based on quantum-mechanical phenomena. Therefore, a shortreview is devoted to (i) quantum bits or qubits (and…
We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…