2,258 research outputs found
On triangular lattice Boltzmann schemes for scalar problems
We propose to extend the d'Humi\'eres version of the lattice Boltzmann scheme
to triangular meshes. We use Bravais lattices or more general lattices with the
property that the degree of each internal vertex is supposed to be constant. On
such meshes, it is possible to define the lattice Boltzmann scheme as a
discrete particle method, without need of finite volume formulation or
Delaunay-Voronoi hypothesis for the lattice. We test this idea for the heat
equation and perform an asymptotic analysis with the Taylor expansion method
for two schemes named D2T4 and D2T7. The results show a convergence up to
second order accuracy and set new questions concerning a possible
super-convergence.Comment: 23 page
Interpolation Methods for Binary and Multivalued Logical Quantum Gate Synthesis
A method for synthesizing quantum gates is presented based on interpolation
methods applied to operators in Hilbert space. Starting from the diagonal forms
of specific generating seed operators with non-degenerate eigenvalue spectrum
one obtains for arity-one a complete family of logical operators corresponding
to all the one-argument logical connectives. Scaling-up to n-arity gates is
obtained by using the Kronecker product and unitary transformations. The
quantum version of the Fourier transform of Boolean functions is presented and
a Reed-Muller decomposition for quantum logical gates is derived. The common
control gates can be easily obtained by considering the logical correspondence
between the control logic operator and the binary propositional logic operator.
A new polynomial and exponential formulation of the Toffoli gate is presented.
The method has parallels to quantum gate-T optimization methods using powers of
multilinear operator polynomials. The method is then applied naturally to
alphabets greater than two for multi-valued logical gates used for quantum
Fourier transform, min-max decision circuits and multivalued adders
Eigenlogic: Interpretable Quantum Observables with applications to Fuzzy Behavior of Vehicular Robots
This work proposes a formulation of propositional logic, named Eigenlogic,
using quantum observables as propositions. The eigenvalues of these operators
are the truth-values and the associated eigenvectors the interpretations of the
propositional system. Fuzzy logic arises naturally when considering vectors
outside the eigensystem, the fuzzy membership function is obtained by the Born
rule of the logical observable.This approach is then applied in the context of
quantum robots using simple behavioral agents represented by Braitenberg
vehicles. Processing with non-classical logic such as multivalued logic, fuzzy
logic and the quantum Eigenlogic permits to enlarge the behavior possibilities
and the associated decisions of these simple agents
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