New PDF release: Mathematical Modeling and Computational Science:

By Gheorghe Adam, Ján Buša, Michal Hnatič

ISBN-10: 3642282113

ISBN-13: 9783642282119

ISBN-10: 3642282121

ISBN-13: 9783642282126

This publication constitutes the refereed post-proceedings of the foreign convention on Mathematical Modeling and Computational Physics, MMCP 2011, held in celebrityá Lesná, Slovakia, in July 2011. The forty-one revised papers offered have been conscientiously reviewed and chosen from quite a few submissions. they're geared up in topical sections on mathematical modeling and strategies, numerical modeling and techniques, computational help of the experiments, computing instruments, and optimization and simulation.

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Additional info for Mathematical Modeling and Computational Science: International Conference, MMCP 2011, Stará Lesná, Slovakia, July 4-8, 2011, Revised Selected Papers

Sample text

1. Simple three-qubit quantum circuit vertical dashed lines in Fig. 1 to show clearly successive steps of the calculation and to emphasize that all the information about the structure of the circuit can be given in the form of the symbolic matrix ⎛ ⎞ 1 1 C 1 CC 1 mat = ⎝ 1 C X C X 1 1 ⎠ . (1) H S 1 S† 1 S H Here the unit means the identical transformation of the qubit, “H” means the Hadamard gate, “C” and “X” in the same column correspond to the control and target qubits of the controlled-NOT gate, S† denotes an adjoint gate for the phase gate S.

Each qubit is a two-level quantum system that can be prepared, manipulated and measured in a controlled way. Traditionally, the state of a qubit is denoted as |a , corresponding to the standard Dirac notation for quantum mechanical states (see [1]). Therefore, a quantum memory register is shown on a diagram visualizing the circuit as a column of states of the form |aj (j = 0, 1, . . , n − 1) from which “quantum wires” start. Although a quantum circuit doesn’t contain any wires as such, the term “wires” is merely used to show evolution of qubits acted on by various quantum gates.

N − 1) with a probability very close to 1, we have √ to repeat Grover’s iteration mopt times, where mopt = round π/(4 arcsin(1/ 32)) − 1/2 = round [7/2]. In the case of a 5-bit integer this value can be equated to 4. Circuit Model of Quantum Computation and Its Simulation a4 H X X H b4 a3 H X X H b3 a2 H X X H b2 a1 H X X H b1 a0 H X X H b0 y Z matG H H H H H 1 X X X X X 1 C C C C Z 1 X X X X X 1 47 H H H ; H H 1 y Fig. 3.

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Mathematical Modeling and Computational Science: International Conference, MMCP 2011, Stará Lesná, Slovakia, July 4-8, 2011, Revised Selected Papers by Gheorghe Adam, Ján Buša, Michal Hnatič


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