title: Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor.
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 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.
authors.affiliation: NMR Quantum Computation and Quantum Information Group, Department of Physics and NMR Research Centre, Indian Institute of Science, Bangalore 560012, India.
authors.forename: Avik
authors.initials: A
authors.lastname: Mitra
authors.forename: Arindam
authors.initials: A
authors.lastname: Ghosh
authors.forename: Ranabir
authors.initials: R
authors.lastname: Das
authors.forename: Apoorva
authors.initials: A
authors.lastname: Patel
authors.forename: Anil
authors.initials: A
authors.lastname: Kumar