895 research outputs found
Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor
Quantum adiabatic algorithm is a method of solving computational problems by
evolving the ground state of a slowly varying Hamiltonian. The technique uses
evolution of the ground state of a slowly varying Hamiltonian to reach the
required output state. In some cases, such as the adiabatic versions of
Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global
adiabatic evolution yields a complexity similar to their classical algorithms.
However, using the local adiabatic evolution, the algorithms given by J. Roland
and N. J. Cerf for Grover's search [ Phys. Rev. A. {\bf 65} 042308(2002)] and
by Saurya Das, Randy Kobes and Gabor Kunstatter for the Deutsch-Jozsa algorithm
[Phys. Rev. A. {\bf 65}, 062301 (2002)], yield a complexity of order
(where N=2 and n is the number of qubits). In this paper we report
the experimental implementation of these local adiabatic evolution algorithms
on a two qubit quantum information processor, by Nuclear Magnetic Resonance.Comment: Title changed, Adiabatic Grover's search algorithm added, error
analysis modifie
Adiabatic Quantum Computation and Deutsch's Algorithm
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's
algorithm can be implemented by an adiabatic quantum computer. We extend our
analysis to the Deutsch-Jozsa problem and estimate the required running time
for both global and local adiabatic evolutions.Comment: 6 Pages, Revtex. Typos corrected, references added. Published versio
Applications of Multi-Valued Quantum Algorithms
This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to
-valued logic using the quantum Fourier transform. Our extended
Deutsch-Jozsa algorithm is not only able to distinguish between constant and
balanced Boolean functions in a single query, but can also find closed
expressions for classes of affine logical functions in quantum oracles,
accurate to a constant term. Furthermore, our multi-valued extension of the
Grover algorithm for quantum database search requires fewer qudits and hence a
substantially smaller memory register, as well as fewer wasted information
states, to implement. We note several applications of these algorithms and
their advantages over the binary cases.Comment: 12 pages, 4 figures; updated version of paper for ISMVL 2007;
contains new proof of multi-valued Grover algorithm time complexity, with
typos correcte
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