Quantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer

Abstract

Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be simulated by a quantum computer. A basis mapping between the systems dictates the average Hamiltonian in the quantum computer needed to implement the desired Hamiltonian in the simulated system. The flexibility of the procedure is illustrated with NMR on ${}^{13}\mathrm{C}$ labeled alanine by creating the nonphysical Hamiltonian ${\ensuremath{\sigma}}_{z}{\ensuremath{\sigma}}_{z}{\ensuremath{\sigma}}_{z}$ corresponding to a three-body interaction.