NMR implementation of adiabatic SAT algorithm using strongly modulated pulses

Abstract

NMR implementation of adiabatic algorithms face severe problems in homonuclear spin systems since the qubit selective pulses are long and during this period, evolution under the Hamiltonian and decoherence cause errors. The decoherence destroys the answer as it causes the final state to evolve to mixed state and in homonuclear systems, evolution under the internal Hamiltonian causes phase errors preventing the initial state to converge to the solution state. The resolution of these issues is necessary before one can proceed to implement an adiabatic algorithm in a large system where homonuclear coupled spins will become a necessity. In the present work, we demonstrate that by using "strongly modulated pulses" (SMPs) for the creation of interpolating Hamiltonian, one can circumvent both the problems and successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. This work also demonstrates that the SMPs tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence, and will be the modality in future implementation of quantum information processing by NMR.