# Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Mitra, Avik and Ghosh, Arindam and Das, Ranabir and Patel, Apoorva and Kumar, Anil (2005) Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor. In: Journal of Magnetic Resonance, 177 (2). pp. 285-298.

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## Abstract

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 [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order \sqrt{N} (where N = $2^{n}$ and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.

Item Type: Journal Article http://dx.doi.org/10.1016/j.jmr.2005.08.... Copyright for this article belongs to Elsevier, Local adiabatic evolution; Grover's search algorithm; Deutsch-Jozsa algorithm; NMR; Quantum information processing Division of Physical & Mathematical Sciences > Centre for High Energy Physics 10 Jan 2006 19 Sep 2010 04:22 http://eprints.iisc.ernet.in/id/eprint/5015