I. Kamleitner

Geometric quantum gates with superconducting qubits

We suggest a scheme to implement a universal set of non-Abelian geometric transformations for a single logical qubit composed of three superconducting 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 qubits. 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.

Adiabatic information transport in the presence of decoherence

We study adiabatic population transfer between discrete positions. Being closely related to stimulated Raman adiabatic passage 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 nonlocal 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.

Geometric phase for an adiabatically evolving open quantum system

We derive a solution for a two-level system evolving adiabatically under the influence of a driving field, which includes open system effects. 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. The dynamic phase can be canceled in the limit of weak coupling to the environment, thereby allowing the geometric phase to be readily extracted both mathematically and operationally.

Quantum position diffusion and its implications for the quantum linear Boltzmann equation

We derive a quantum master equation from first principles to describe friction in one dimensional, collisional Brownian motion. We are the first to avoid an ill-defined square of the Dirac delta function by using localized wave packets rather than plane waves. Solving the Schrödinger equation for two colliding particles, we discover that the previously found position diffusion is not a physical process, but an artifact of the approximation of a coarse grained time scale.

Full counting statistics applied to dissipative Cooper pair pumping

We calculate the charge transport in a flux biased dissipative Cooper pair pump using the method of full counting statistics (FCS). This is instead of a more traditional technique of integrating a very small expectation value of the instantaneous current over the pumping period. We show that the rotating wave approximation (RWA), which fails in the traditional technique, produces accurate results within the FCS method.

Coherent Cooper-pair pumping by magnetic flux control

We introduce and discuss a scheme for Cooper-pair pumping. The scheme relies on the coherent transfer of a superposition of charge states across a superconducting island and is realized by adiabatic manipulation of magnetic fluxes. Differently from previous implementations, it does not require any modulation of electrostatic potentials. We find a peculiar dependence of the pumped charge on the superconducting phase bias across the pump and that an arbitrarily large amount of charge can be pumped in a single cycle when the phase bias is {\pi}. We explain these features and their relation to the adiabatic theorem.

Time-dependent Markovian master equation for adiabatic systems and its application to Cooper-pair pumping

For adiabatically and periodically manipulated dissipative quantum systems we derive, using Floquet theory, a simple Markovian master equation. Contrary to some previous works we explicitly take into account the time dependence of the Hamiltonian and, therefore, obtain a master equation with a time-dependent dissipative part. We illustrate our theory with two examples and compare our results with the previously proposed master equations. In particular, we consider the problem of Cooper pair pumping and demonstrate the inadequacy of the secular (rotating wave) approximation when calculating the pumped charge. The secular approximation producing a master equation of the Lindblad type approximates well the quantum state (density matrix) of the system, while to determine the pumped charge a non-Lindblad master equation beyond the rotating wave approximation is necessary.

Collisional decoherence of a tracer particle moving in one dimension

We study decoherence of the external degree of freedom of a tracer particle moving in a one-dimensional dilute Boltzmann gas. We find that phase averaging is the dominant decoherence effect, rather than information exchange between tracer and gas particles. While a coherent superposition of two wave packets with different mean positions quickly turns into a mixed state, it is demonstrated that such superpositions of different momenta are robust to phase averaging, until the two wave packets acquire a different position due to the different velocity of each wave packet.