Chapter 6 Groups and Representations in Quantum Mechanics
... The direct product provides a way of enlarging the number of elements in a group while retaining the group properties. Direct products occur in several contexts. For example, if a Hamiltonian or Lagrangian contains different types of coordinates, such as spatial coordinates for different particles, ...
... The direct product provides a way of enlarging the number of elements in a group while retaining the group properties. Direct products occur in several contexts. For example, if a Hamiltonian or Lagrangian contains different types of coordinates, such as spatial coordinates for different particles, ...
A Bird`s-Eye View of Density-Functional Theory
... One sometimes says that T̂ and Û are ‘universal’, while V̂ is systemdependent, or ‘nonuniversal’. We will come back to this terminology. A simple estimate of the computational complexity of this task is to imagine a real-space representation of Ψ on a mesh, in which each coordinate is discretized b ...
... One sometimes says that T̂ and Û are ‘universal’, while V̂ is systemdependent, or ‘nonuniversal’. We will come back to this terminology. A simple estimate of the computational complexity of this task is to imagine a real-space representation of Ψ on a mesh, in which each coordinate is discretized b ...
On quantum detection and the square
... bility of a detection error when the states exhibit certain symmetries [7]; it is “pretty good” when the states to be distinguished are equally likely and almost orthogonal [9]; and it is asymptotically optimal [10]. Because of these properties, the SRM has been employed as a detection measurement i ...
... bility of a detection error when the states exhibit certain symmetries [7]; it is “pretty good” when the states to be distinguished are equally likely and almost orthogonal [9]; and it is asymptotically optimal [10]. Because of these properties, the SRM has been employed as a detection measurement i ...
The Age of Entanglement Quantum Computing the (Formerly) Uncomputable
... photodetector called a CCD (charge-coupled device) used in your video camera. When we turn on the experiment, the photo-plate responds at the positions where it records a photon. After only several photons have been detected, the photo-plate may look like Fig. 9.2a. No discernible pattern of bright ...
... photodetector called a CCD (charge-coupled device) used in your video camera. When we turn on the experiment, the photo-plate responds at the positions where it records a photon. After only several photons have been detected, the photo-plate may look like Fig. 9.2a. No discernible pattern of bright ...
Application of Quantum Computing principles to Natural Language Processing
... a broad analysis of various search and optimization techniques used classically in NLP. The intent of this section is two-fold. First, the unfamiliar reader can familiarize himself about the presented techniques. Secondly, we study the theoretical aspects of these techniques in detail to gain deeper ...
... a broad analysis of various search and optimization techniques used classically in NLP. The intent of this section is two-fold. First, the unfamiliar reader can familiarize himself about the presented techniques. Secondly, we study the theoretical aspects of these techniques in detail to gain deeper ...
Perfect state transfer over distance
... think about more complicated spin networks than the linear chain or chains with preengineered nearest-neighbor interaction strengths. We provide two alternative methods for understanding how perfect state transfer is achieved with preengineered couplings. This paper expands and extends the work done ...
... think about more complicated spin networks than the linear chain or chains with preengineered nearest-neighbor interaction strengths. We provide two alternative methods for understanding how perfect state transfer is achieved with preengineered couplings. This paper expands and extends the work done ...
The Relation Between Classical and Quantum Mechanical Rigid
... Conditions are given on a quantum-mechanical system which effectively reduce the Hamiltonian to a rigid body Hamiltonian derived with classical mechanics. ...
... Conditions are given on a quantum-mechanical system which effectively reduce the Hamiltonian to a rigid body Hamiltonian derived with classical mechanics. ...
Quantum Thermodynamics: A Dynamical Viewpoint
... 4. The I-Law The I-law is devoted to the elusive concept of energy conservation. If the universe is closed and passive, meaning there are no source terms, then its energy is conserved. This implies that the total evolution is unitary, where the dynamics are generated by a total Hamiltonian, Ĥ, cf. ...
... 4. The I-Law The I-law is devoted to the elusive concept of energy conservation. If the universe is closed and passive, meaning there are no source terms, then its energy is conserved. This implies that the total evolution is unitary, where the dynamics are generated by a total Hamiltonian, Ĥ, cf. ...
A short introduction to unitary 2-designs
... for all possible pt , where the integral is taken with respect to the normalized spherical measure. Note that by definition, a t-design is also a (t − 1)-design, since all monomials can have degree at most t (as long as all degrees are identical). Spherical designs exist for all t and d [1]. Let us ...
... for all possible pt , where the integral is taken with respect to the normalized spherical measure. Note that by definition, a t-design is also a (t − 1)-design, since all monomials can have degree at most t (as long as all degrees are identical). Spherical designs exist for all t and d [1]. Let us ...
by Chao Shen - Deep Blue
... Quantum technology with atomic, molecular and optical systems has advanced to a stage that single particles can be manipulated precisely so that quantum information processing is no longer elusive. In fact, a great number of quantum information protocols have been demonstrated with small scaled syst ...
... Quantum technology with atomic, molecular and optical systems has advanced to a stage that single particles can be manipulated precisely so that quantum information processing is no longer elusive. In fact, a great number of quantum information protocols have been demonstrated with small scaled syst ...
Tight bounds on quantum searching
... A = {i | T [i] = x} and B = {i | T [i] 6= x}. The key observation is that the value of θ, and therefore that of t, can be inferred directly from the period of the function that sends j onto kj . This period can be estimated from sampling in a discrete Fourier transform of the function. In order to p ...
... A = {i | T [i] = x} and B = {i | T [i] 6= x}. The key observation is that the value of θ, and therefore that of t, can be inferred directly from the period of the function that sends j onto kj . This period can be estimated from sampling in a discrete Fourier transform of the function. In order to p ...
Computational Complexity: A Modern Approach
... quantum mechanics, the probability waves are associated not just with single particles, but also by any collection of particles (such as humans!). This interaction of probability waves corresponding to collections of particles is key to the power of quantum computing, and underlies the apparent expo ...
... quantum mechanics, the probability waves are associated not just with single particles, but also by any collection of particles (such as humans!). This interaction of probability waves corresponding to collections of particles is key to the power of quantum computing, and underlies the apparent expo ...
research statement - University of Illinois at Chicago
... GP hierarchy are determined by solutions to a quintic NLS. In such a way, they derived the quintic NLS from quantum many-body systems. In the same paper [4], T. Chen-Pavlović predicted that, if both two-body and three-body interactions are present in the model, then this would produce an NLS with l ...
... GP hierarchy are determined by solutions to a quintic NLS. In such a way, they derived the quintic NLS from quantum many-body systems. In the same paper [4], T. Chen-Pavlović predicted that, if both two-body and three-body interactions are present in the model, then this would produce an NLS with l ...
Aspects of quantum information theory
... this end the text is divided into two parts. The first (Part I. “Fundamentals”) is of introductory nature. It takes into account that most of the fundamental concepts and basic ideas of quantum information are developed during the last decade, and are therefore unfamiliar to most physicists. To make ...
... this end the text is divided into two parts. The first (Part I. “Fundamentals”) is of introductory nature. It takes into account that most of the fundamental concepts and basic ideas of quantum information are developed during the last decade, and are therefore unfamiliar to most physicists. To make ...
Quantum neural networks
... • Many universes (many-world) interpretation of Everett [6], etc. The choice of interpretation is important in establishing different analogies between quantum physics and neurocomputing. The field of neural networks contains several important basic ideas, which include the concept of a processing e ...
... • Many universes (many-world) interpretation of Everett [6], etc. The choice of interpretation is important in establishing different analogies between quantum physics and neurocomputing. The field of neural networks contains several important basic ideas, which include the concept of a processing e ...
On Zurek`s Derivation of the Born Rule
... with respect to any orthonormal basis can be physically motivated by remembering that any orthonormal basis {v1 , . . . , vn } can be viewed as the = i λi |vi vi |, and by referring to the fact eigenbasis of observables O on a system with state that in every measurement of such an observable ...
... with respect to any orthonormal basis can be physically motivated by remembering that any orthonormal basis {v1 , . . . , vn } can be viewed as the = i λi |vi vi |, and by referring to the fact eigenbasis of observables O on a system with state that in every measurement of such an observable ...
Roland Katz –15/01/2015
... Conclusion First tests passed with success Relevant suppression pattern related to experimental observations: thermal effects -> less suppression of J/y, y‘… RAA (J/y) > RAA (y’) for T>0.25 GeV ...
... Conclusion First tests passed with success Relevant suppression pattern related to experimental observations: thermal effects -> less suppression of J/y, y‘… RAA (J/y) > RAA (y’) for T>0.25 GeV ...