8,420 research outputs found
A Heuristic Procedure with Guided Reproduction for Constructing Cocyclic Hadamard Matrices
A genetic algorithm for constructing cocyclic Hadamard matrices
over a given group is described. The novelty of this algorithm is
the guided heuristic procedure for reproduction, instead of the classical
crossover and mutation operators. We include some runs of the algorithm
for dihedral groups, which are known to give rise to a large amount of
cocyclic Hadamard matrices.Ministerio de Ciencia e InnovaciĂłn MTM2008-06578Junta de AndalucĂa FQMâ296Junta de AndalucĂa P07-FQM-0298
The problem of mutually unbiased bases in dimension 6
We outline a discretization approach to determine the
maximal number of mutually unbiased bases in dimension 6. We
describe the basic ideas and introduce the most important definitions
to tackle this famous open problem which has been open for
the last 10 years. Some preliminary results are also listed
Universal Programmable Quantum Circuit Schemes to Emulate an Operator
Unlike fixed designs, programmable circuit designs support an infinite number
of operators. The functionality of a programmable circuit can be altered by
simply changing the angle values of the rotation gates in the circuit. Here, we
present a new quantum circuit design technique resulting in two general
programmable circuit schemes. The circuit schemes can be used to simulate any
given operator by setting the angle values in the circuit. This provides a
fixed circuit design whose angles are determined from the elements of the given
matrix-which can be non-unitary-in an efficient way. We also give both the
classical and quantum complexity analysis for these circuits and show that the
circuits require a few classical computations. They have almost the same
quantum complexities as non-general circuits. Since the presented circuit
designs are independent from the matrix decomposition techniques and the global
optimization processes used to find quantum circuits for a given operator, high
accuracy simulations can be done for the unitary propagators of molecular
Hamiltonians on quantum computers. As an example, we show how to build the
circuit design for the hydrogen molecule.Comment: combined with former arXiv:1207.174
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