Related papers: Examples of quantum integrals
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
We discuss whether, to what extent and how a quantum computing device can be evaluated and simulated using classical tools.
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
The concept of a quantum algebra is made easy through the investigation of the prototype algebras $u_{qp}(2)$, $su_q(2)$ and $u_{qp}(1,1)$. The latter quantum algebras are introduced as deformations of the corresponding Lie algebras~; this…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
After a brief introduction to the principles and promise of quantum information processing, the requirements for the physical implementation of quantum computation are discussed. These five requirements, plus two relating to the…
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of…
Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various…
We implement in a reactive programming framework a simulation of three aspects of quantum mechanics: self-interference, state superposition, and entanglement. The simulation basically consists in a cellular automaton embedded in a…
Research on quantum technology spans multiple disciplines: physics, computer science, engineering, and mathematics. The objective of this manuscript is to provide an accessible introduction to this emerging field for economists that is…
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…
Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the Zeno effect. Dynamical and…
The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of…
Quantum cryptography is reviewed, first using entanglement both for the intuition and for the experimental realizations. Next, the implementation is simplified in several steps until it becomes practical. At this point entanglement has…
Quantum computation using electron spins in three coupled dot with different size is proposed. By using the energy selectivity of both photon assisted tunneling and spin rotation of electrons, logic gates are realized by static and…