THE K-THEORY OF FREE QUANTUM GROUPS 1. Introduction A
... for matrices Pi ∈ GLmi (C) and Qj ∈ GLnj (C) such that Qj Qj = ±1. Here FU (P ) and FO(Q) are the free unitary and free orthogonal quantum groups, which were first introduced by Wang and Van Daele [34], [29] with a different notation. The special case l = 0 and P1 = · · · = Pk = 1 ∈ GL1 (C) of this ...
... for matrices Pi ∈ GLmi (C) and Qj ∈ GLnj (C) such that Qj Qj = ±1. Here FU (P ) and FO(Q) are the free unitary and free orthogonal quantum groups, which were first introduced by Wang and Van Daele [34], [29] with a different notation. The special case l = 0 and P1 = · · · = Pk = 1 ∈ GL1 (C) of this ...
Quantum Tweezer for Atoms
... probability of finding no atoms (dashed), one atom (dotted), and two atoms (solid lines) in the dot as a function of position for three different speeds of the dot. The top panel shows the adiabatic result, obtained for v, that is several orders of magnitude smaller than the smallest speed in Fig. 2 ...
... probability of finding no atoms (dashed), one atom (dotted), and two atoms (solid lines) in the dot as a function of position for three different speeds of the dot. The top panel shows the adiabatic result, obtained for v, that is several orders of magnitude smaller than the smallest speed in Fig. 2 ...
Toward Quantum Computational Agents.
... The Hadamard gate creates a superposed qubit state for standard basis states, demonstrates destructive quantum interference if applied to superposed quantum states (MH ( √12 (|0 > +|1 >)) = |0 >), and can be physically realized, for example, by a 50/50-beamsplitter in a Mach-Zehnder interferometer [ ...
... The Hadamard gate creates a superposed qubit state for standard basis states, demonstrates destructive quantum interference if applied to superposed quantum states (MH ( √12 (|0 > +|1 >)) = |0 >), and can be physically realized, for example, by a 50/50-beamsplitter in a Mach-Zehnder interferometer [ ...
Quantum computing Markus Kiili Opinnäytetyö
... This means that the energies are not so large that particle production from kinetic energy is meaningful. Different physical states of a quantum mechanical system are described by a vector in a complex linear space called a Hilbert space. 3.1.1 Complex numbers ℂ Complex numbers have the following pr ...
... This means that the energies are not so large that particle production from kinetic energy is meaningful. Different physical states of a quantum mechanical system are described by a vector in a complex linear space called a Hilbert space. 3.1.1 Complex numbers ℂ Complex numbers have the following pr ...
Is the dynamics of open quantum systems always linear?
... always linear. It simply acts as the multiplication by the reference environment density operator B. In the case of a classical system dynamics the role of density matrices is taken over by probability densities defined on the respective phase space. Then, any preparation can be characterized by a ...
... always linear. It simply acts as the multiplication by the reference environment density operator B. In the case of a classical system dynamics the role of density matrices is taken over by probability densities defined on the respective phase space. Then, any preparation can be characterized by a ...
Anyons and the quantum Hall effect— A pedagogical
... Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel ...
... Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel ...
Superconducting Circuits and Quantum Computation T. P. Orlando
... of quantum gates of quantum computation. But qubit interaction also introduces operational errors by additional transition matrix elements during gate operations. By mapping the interacting qubits as a multilevel quantum system with higher levels, the same method can be applied to correct the errors ...
... of quantum gates of quantum computation. But qubit interaction also introduces operational errors by additional transition matrix elements during gate operations. By mapping the interacting qubits as a multilevel quantum system with higher levels, the same method can be applied to correct the errors ...
Nonequilibrium entropy production in open and closed quantum
... At its origins the theory of thermodynamics was developed to understand and improve heat engines. Hence, special interest lies on the dynamical properties of energy conversion processes. However, the original theory was only able to predict the behavior of physical systems by considering their macro ...
... At its origins the theory of thermodynamics was developed to understand and improve heat engines. Hence, special interest lies on the dynamical properties of energy conversion processes. However, the original theory was only able to predict the behavior of physical systems by considering their macro ...
Nonlinear electron acceleration by oblique whistler waves - HAL-Insu
... and does not vary substantially at k > 20 . Such a behavior can be explained by a combination of two processes: (1) with propagation away from the equator, waves become more intense due to a local instability of the background plasma medium, (2) wave propagation in the inhomogeneous magnetic field ...
... and does not vary substantially at k > 20 . Such a behavior can be explained by a combination of two processes: (1) with propagation away from the equator, waves become more intense due to a local instability of the background plasma medium, (2) wave propagation in the inhomogeneous magnetic field ...
DERIVATIONS, DIRICHLET FORMS AND SPECTRAL ANALYSIS
... where the latter encodes the Leibniz rule (see Lemma 3.2.5 and Theorem 3.2.2 of [FOT]). The measure νa = νa,a is positive and is called the energy measure of a. Note that in the classical theory dνa,b = ∇a · ∇b dm where dm is Lebesgue measure. The energy measures do not directly produce a Hilbert mo ...
... where the latter encodes the Leibniz rule (see Lemma 3.2.5 and Theorem 3.2.2 of [FOT]). The measure νa = νa,a is positive and is called the energy measure of a. Note that in the classical theory dνa,b = ∇a · ∇b dm where dm is Lebesgue measure. The energy measures do not directly produce a Hilbert mo ...
Dynamical Aspects of Information Storage in Quantum
... In this respect, the assumption of finite precision of all physically realizable state preparation, manipulation, and registration procedures is particularly important, and can even be treated as an empirical given. This premise is general enough to subsume (a) fundamental limitations imposed by the ...
... In this respect, the assumption of finite precision of all physically realizable state preparation, manipulation, and registration procedures is particularly important, and can even be treated as an empirical given. This premise is general enough to subsume (a) fundamental limitations imposed by the ...
Path Integral Monte Carlo Zachary Wolfson
... confirmed experimentally by Carl Anderson in 1932, becoming the first example of antimatter and opening the door to the field of elementary particle physics.( 5) The same year that Anderson discovered the positron, he predicted that, due to the Coulomb attraction between a positron and electron, the ...
... confirmed experimentally by Carl Anderson in 1932, becoming the first example of antimatter and opening the door to the field of elementary particle physics.( 5) The same year that Anderson discovered the positron, he predicted that, due to the Coulomb attraction between a positron and electron, the ...
Photodissociation Dynamics of Molecular Fluorine in an Argon
... the host matrix, in the time domain of a few hundred femtoseconds. For this purpose we employ a variant of quantumclassical surface hopping techniques,24 which treats the nuclear dynamics classically while the laser-induced transitions between adiabatic electronic states are simulated quantum-mechan ...
... the host matrix, in the time domain of a few hundred femtoseconds. For this purpose we employ a variant of quantumclassical surface hopping techniques,24 which treats the nuclear dynamics classically while the laser-induced transitions between adiabatic electronic states are simulated quantum-mechan ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.