A Hybrid Architecture Approach for Quantum Algorithms

Aghaei, Mohammad Reza Soltan; Zukarnain, Zuriati Ahmad; Mamat, Ali; Zainuddin, Hishamuddin

doi:10.3844/jcssp.2009.725.731

Cited by 4 publications

(1 citation statement)

References 12 publications

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“…Making use of fractional derivatives and integrals, one may describe more accurately a complex system and accordingly investigate more completely its dynamical and physical properties. Although fractional calculus has been studied for over 300 years, it has been regarded principally as a mathematical curiosity until about 1992, where fractional dynamical equations were pretty much restricted to the realm of mathematics and engineering including hydrology, viscoelastivity, heat conduction, polymer physics, chaos and EL-NABULSI Ahmad Rami fractals, control theory, plasma physics, wave propagation in complex and porous media, astrophysics, cosmology, quantum field theory, potential theory and so on (Aghaei et al, 2009;Samko et al, 1993;Miller and Ross, 1993;Podlubny, 1999;Hilfer, 2000;Kluwer, 2004;Ortigueira and Machado, 2006;2008;El-Nabulsi, 2008a;2009a). Actually, there exist numerous different forms of fractional integral and derivatives operators and the definition of the fractional order derivative and integral are not unique where several definitions exist, e.g., Grunwald-Letnikov, Caputo, Weyl, Feller, ErdelyiKober, Riesz, Saxena, Kumbhat, Kiryakova, Srivastava and Raina.…”

Section: Introductionmentioning

confidence: 99%

Fractional Quantum Field Theory on Multifractals Sets

Rami¹

2011

American Journal of Engineering and Applied Sciences

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Problem statement:This study is a contribution to the general program of describing complex dynamical systems using the tool of fractional calculus of variations. Approach: Following our previous work, fractional quantum field theory based on the fractional actionlike variational approach supported by Saxena-Kumbhat fractional integrals functionals, fractional derivative of order (α, β) and dynamical fractional exponent on multi-fractal sets is considered. Results: In order to build the required theory, we introduce the Saxena-Kumbhat hypergeometric fractional functionals determined on the functions on a multifractal sets. We prove, developing the corresponding fractional calculus of variations, that a hierarchy of differential equations can be developed from the extended fractional Lagrangian formalism. Besides, a generalization of the resulting Hamiltonian and Lagrangian dynamics on the complex plane is addressed. Conclusion: The new complexified dynamics guides to a new dynamics which may differ totally from the classical mechanics cardinally and may bring new appealing consequences. Some additional interesting results are explored and discussed in some details.

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Section: Introductionmentioning

confidence: 99%

Fractional Quantum Field Theory on Multifractals Sets

Rami¹

2011

American Journal of Engineering and Applied Sciences

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Model of a hybrid processor executing C++ with additional quantum functions

Elhoushi

El-Kharashi

Elrefaei

2014

Microprocessors and Microsystems

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Circuit design for clique problem and its implementation on quantum computer

Sanyal¹,

Saha²,

Saha³

et al. 2021

IET Quantum Communication

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Finding cliques in a graph has a wide range of applications due to its pattern matching ability. The k‐clique problem, a subset of the clique problem, determines whether or not an arbitrary network has a clique of size k. Modern‐day applications include a variation of the k‐clique problem that lists all cliques of size k. However, the quantum implementation of such a variation of the k‐clique problem has not been addressed yet. In this work, apart from the theoretical solution of such a k‐clique problem, practical quantum‐gate‐based implementation has been addressed using Grover's algorithm. In a classical‐quantum hybrid architecture, this approach is extended to build the circuit for the maximum clique problem. Our technique is generalised since the program automatically builds the circuit for any given undirected and unweighted graph and any chosen k. For a small k with regard to a big graph, the proposed solution to addressing the k‐clique issue has shown a reduction in qubit cost and circuit depth when compared to the state‐of‐the‐art approach. A framework is also presented for mapping the automated generated circuit for clique problems to quantum devices. Using IBM's Qiskit, an analysis of the experimental results is demonstrated.

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A Hybrid Architecture Approach for Quantum Algorithms

Cited by 4 publications

References 12 publications

Fractional Quantum Field Theory on Multifractals Sets

Fractional Quantum Field Theory on Multifractals Sets

Model of a hybrid processor executing C++ with additional quantum functions

Circuit design for clique problem and its implementation on quantum computer

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