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Sep 22, 2013
09/13

by
Goong Chen; Zijian Diao

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Consider the unstructured search of an unknown number l of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's single-object search algorithm to the multi-object case and the second part is to solve a counting problem to determine l. In this paper, we study the multi-object quantum search algorithm (in continuous time), but in a more structured way by taking into account the...

Source: http://arxiv.org/abs/quant-ph/0011019v2

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Sep 17, 2013
09/13

by
Goong Chen; Shunhua Sun

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There are major advantages in a newer version of Grover's quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject search. We show the techniques to achieve the reduction of the problem to one on an invariant subspace of dimension just equal to two.

Source: http://arxiv.org/abs/quant-ph/0007124v1

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Sep 17, 2013
09/13

by
Goong Chen; Stephen A. Fulling; Jeesen Chen

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L. K. Grover's search algorithm in quantum computing gives an optimal, quadratic speedup in the search for a single object in a large unsorted database. In this paper, we generalize Grover's algorithm in a Hilbert-space framework for both continuous and discrete time cases that isolates its geometrical essence to the case where more than one object satisfies the search criterion.

Source: http://arxiv.org/abs/quant-ph/0007123v1

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Sep 17, 2013
09/13

by
Charles M. Bowden; Goong Chen; Zijian Diao; Andreas Klappenecker

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The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the two-dimensional 1-qubit space. In this paper, we show that H and P(.) suffice to generate the unitary group U(2) and, consequently, through controlled-U operations and their concatenations, the entire unitary group U(2^n) on n-qubits can be generated. Since any...

Source: http://arxiv.org/abs/quant-ph/0007122v1

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Jun 29, 2018
06/18

by
Tai-Chia Lin; Milivoj R. Belic; Milan S. Petrovic; Hichem Hajaiej; Goong Chen

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The virial theorem is a nice property for the linear Schrodinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrodinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the...

Topics: Nonlinear Sciences, Analysis of PDEs, Physics, Mathematics, Pattern Formation and Solitons, Optics,...

Source: http://arxiv.org/abs/1608.06102

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Sep 21, 2013
09/13

by
Goong Chen; Siu A. Chin; Yusheng Dou; Kishore T. Kapale; Moochan Kim; Anatoly A. Svidzinsky; Kerim Urtekin; Han Xiong; Marlan O. Scully

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In this review we first discuss extension of Bohr's 1913 molecular model and show that it corresponds to the large-D limit of a dimensional scaling (D-scaling) analysis, as developed by Herschbach and coworkers. In a separate but synergetic approach to the two-electron problem, we summarize recent advances in constructing analytical models for describing the two-electron bond. The emphasis here is not maximally attainable numerical accuracy, but beyond textbook accuracy as informed by physical...

Source: http://arxiv.org/abs/physics/0508177v1