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

• Published in: Journal of magnetic resonance (1997) Vol. 177; no. 2; pp. 285 - 298
• Main Authors: Mitra, Avik, Ghosh, Arindam, Das, Ranabir, Patel, Apoorva, Kumar, Anil
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.12.2005
• Subjects: Deutsch–Jozsa algorithm; Grover’s search algorithm; Local adiabatic evolution; NMR; Quantum information processing; Deutsch–Jozsa algorithm; NMR; Local adiabatic evolution; Quantum information processing; Grover’s search algorithm
• ISSN: 1090-7807; 1096-0856
• DOI: 10.1016/j.jmr.2005.08.004

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.