Momentum Maps, Dual Pairs and Reduction in
... If J is a momentum map for a weakly hamiltonian action ψ, then J([v, w]) and {J(v), J(w)} are both hamiltonians corresponding to the vector field [v, w]M . Thus, since we are assuming M connected, we have c(v, w) = J([v, w]) − {J(v), J(w)} ∈ R. Note that c defines a skew-symmetric bilinear form on g ...
... If J is a momentum map for a weakly hamiltonian action ψ, then J([v, w]) and {J(v), J(w)} are both hamiltonians corresponding to the vector field [v, w]M . Thus, since we are assuming M connected, we have c(v, w) = J([v, w]) − {J(v), J(w)} ∈ R. Note that c defines a skew-symmetric bilinear form on g ...
Some Quantum Computational Circuits
... compared to classical objects such as billiard balls or integrated circuits, and so to understand how they are designed, we need to understand quantum physics rather than classical physics since it is quantum physics that describes these small entities. There’s some surprising behaviour to be had at ...
... compared to classical objects such as billiard balls or integrated circuits, and so to understand how they are designed, we need to understand quantum physics rather than classical physics since it is quantum physics that describes these small entities. There’s some surprising behaviour to be had at ...
Quantum Computing and Parallel (Multicore) Processing
... compared to classical objects such as billiard balls or integrated circuits, and so to understand how they are designed, we need to understand quantum physics rather than classical physics since it is quantum physics that describes these small entities. There’s some surprising behaviour to be had at ...
... compared to classical objects such as billiard balls or integrated circuits, and so to understand how they are designed, we need to understand quantum physics rather than classical physics since it is quantum physics that describes these small entities. There’s some surprising behaviour to be had at ...
Lecture Notes of my Course on Quantum Computing
... to the circuits are random vectors. Circuits naturally act on probability distributions, and this is an example of a push-forward measure. We, however, will need a matrix representation of this action. Any reversible computation is equivalent to the action of a permutation matrix on a probability ve ...
... to the circuits are random vectors. Circuits naturally act on probability distributions, and this is an example of a push-forward measure. We, however, will need a matrix representation of this action. Any reversible computation is equivalent to the action of a permutation matrix on a probability ve ...
Tree Search and Quantum Computation
... branching factor? Clearly, this is not always the case for the complete set of problems that can potentially be addressed by search algorithms. When considering a non-constant branching factor, what would be the associated impacts in overall system performance? Additionally, traditional search strat ...
... branching factor? Clearly, this is not always the case for the complete set of problems that can potentially be addressed by search algorithms. When considering a non-constant branching factor, what would be the associated impacts in overall system performance? Additionally, traditional search strat ...
Quantum Probability Quantum Information Theory Quantum
... According to such ‘realistic’ intuitions all things have their definite place and properties, such as speed, colour, weight, etcetera. Quantum theory, however, refuses to precisely pinpoint them. Now it could be, of course, that quantum theory is just incomplete, that it gives a coarse description o ...
... According to such ‘realistic’ intuitions all things have their definite place and properties, such as speed, colour, weight, etcetera. Quantum theory, however, refuses to precisely pinpoint them. Now it could be, of course, that quantum theory is just incomplete, that it gives a coarse description o ...
PDF: Aspden et al 2016 b
... beyond considerations of measurement-induced perturbations and is rooted in an inherent uncertainty associated with the particle itself. In terms of the philosophical debate, rather than the “which slit” question it is the mechanism by which the extended photon wavefunction is collapsed (or projecte ...
... beyond considerations of measurement-induced perturbations and is rooted in an inherent uncertainty associated with the particle itself. In terms of the philosophical debate, rather than the “which slit” question it is the mechanism by which the extended photon wavefunction is collapsed (or projecte ...
Quantum Entanglement in Many-body Systems
... Here I would like to mention about the recent debates about this issue. In [14], it is claimed that under certain conditions, first-order (second-order) phase transition happens if and only if the (first order derivative of the) ground state concurrence has discontinuity or divergence. However, in [ ...
... Here I would like to mention about the recent debates about this issue. In [14], it is claimed that under certain conditions, first-order (second-order) phase transition happens if and only if the (first order derivative of the) ground state concurrence has discontinuity or divergence. However, in [ ...
Quantum Computers that can be Simulated Classically in
... produce di erent overlap parity for the given external edge and the various internal matchings depending on whether the omittable node was in the matching.) To verify this note that if for i 2 X \ Z there are r nodes j < i where j 2 V Z , then the parity of the overlap of the external edge from i wi ...
... produce di erent overlap parity for the given external edge and the various internal matchings depending on whether the omittable node was in the matching.) To verify this note that if for i 2 X \ Z there are r nodes j < i where j 2 V Z , then the parity of the overlap of the external edge from i wi ...
Phys. Rev. Lett
... Analogously to the previous analysis, the experimental Poincaré sphere vectors obtained after the l ! conversion are reported in Fig. 2(d). Such transferrer can be, for example, exploited within a measurement apparatus for analyzing both and l degrees of freedom without using holograms, with an ...
... Analogously to the previous analysis, the experimental Poincaré sphere vectors obtained after the l ! conversion are reported in Fig. 2(d). Such transferrer can be, for example, exploited within a measurement apparatus for analyzing both and l degrees of freedom without using holograms, with an ...
URL - StealthSkater
... scattering solutions of Schrödinger equation. It seems, however, impossible to assign any real Scrödinger time evolution with U. In Zero Energy Ontology, U defines a unitary matrix between zero energy states and is naturally assignable to intentional actions whereas the ordinary S-matrix telling wha ...
... scattering solutions of Schrödinger equation. It seems, however, impossible to assign any real Scrödinger time evolution with U. In Zero Energy Ontology, U defines a unitary matrix between zero energy states and is naturally assignable to intentional actions whereas the ordinary S-matrix telling wha ...
