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We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…
We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
We propose a scheme for implementing quantum algorithms with resonant interactions. Our scheme only requires resonant interactions between two atoms and a cavity mode, which is simple and feasible. Moreover, the implementation would be an…
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
Results gained for electron scattering on $^3$He in a nonrelativistic framework are reviewed. The electromagnetic current is truncated to a single nucleon operator, but the interaction among the three nucleons is treated exactly. Thus…
It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…
We develop a theoretical framework for the exploration of quantum mechanical coherent population transfer phenomena, with the ultimate goal of constructing faithful models of devices for classical and quantum information processing…
Color transparency is the proposal that under certain circumstances the strong interactions can be reduced in magnitude. We give a comprehensive review of the physics, which hinges on the interface of perturbative QCD with non--perturbative…
We formulate the $O(3)$ non-linear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
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…
Using modern nucleon-nucleon interactions in the description of the $A=3,4$ nuclei, it is not possible to reproduce both the three- and four-nucleon binding energies simultaneously. This is one manifestation of the necessity of including a…
The WKB approximation of geometrical optics is widely used in plasma physics, quantum mechanics and reduced wave modeling in general. However, it is well-known that the approximation breaks down at focal and turning points. In this work we…
We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by…
Using the highly detuned interaction between three-level $\Lambda$-type atoms and coherent optical fields, we can realize the C-NOT gates from atoms to atoms, optical fields to optical fields, atoms to optical fields and optical fields to…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…