No abstract

We suggest a scheme to implement a universal set of non-Abelian geometric transformations for a single logical qubit composed of three superconducting transmon qubits coupled to a single cavity. The scheme utilizes an adiabatic evolution in a rotating frame induced by the effective tripod Hamiltonian which is achieved by longitudinal driving of the transmons. The proposal is experimentally feasible with the current state of the art and could serve as a first proof of principle for geometric quantum computing.Comment: 7 pages, 5 figure

We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution, which is obtained by working in the representation corresponding to the eigenstates of the time-dependent Hermitian Hamiltonian, enables the dynamic and geometric phases of the evolving density matrix to be separated and relatively easily calculated.

We study adiabatic population transfer between discrete positions. Being closely related to STIRAP in optical systems, this transport is coherent and robust against variations of experimental parameters. Thanks to these properties the scheme is a promising candidate for transport of quantum information in quantum computing. We study the effects of spatially registered noise sources on the quantum transport and in particular model Markovian decoherence via non-local coupling to nearby quantum point contacts which serve as information readouts. We find that the rate of decoherence experienced by a spatial superposition initially grows with spatial separation but surprisingly then plateaus. In addition we include non-Markovian effects due to couplings to nearby two level systems and we find that although the population transport exhibits robustness in the presence of both types of noise sources, the transport of a spatial superposition exhibits severe fragility.Comment: 11page