Transferring the state of an information carrier from a sender to a receiver
is an essential primitive in both classical and quantum communication and
information processing. In a quantumprocess known as teleportation the unknown
state of a quantum bit can be relayed to a distant party using shared
entanglement and classical information. Here we present experiments in a
solid-state system based on superconducting quantum circuits demonstrating the
teleportation of the state of a qubit at the macroscopic scale. In our
experiments teleportation is realized deterministically with high efficiency
and achieves a high rate of transferred qubit states. This constitutes a
significant step towards the realization of repeaters for quantum communication
at microwave frequencies and broadens the tool set for quantum information
processing with superconducting circuits.
We make use of a superconducting qubit to study the effects of noise on
adiabatic geometric phases. The state of the system, an effective spin one-half
particle, is adiabatically guidedalong a closed path in parameter space and
thereby acquires a geometric phase. By introducing artificial fluctuations in
the control parameters, we measure the geometric contribution to dephasing for
a variety of noise powers and evolution times. Our results clearly show that
only fluctuations which distort the path lead to geometric dephasing. In a
direct comparison with the dynamic phase, which is path-independent, we observe
that the adiabatic geometric phase is less affected by noise-induced dephasing.
This observation directly points towards the potential of geometric phases for
quantum gates or metrological applications.
Geometric phases, which accompany the evolution of a quantum system and
depend only on its trajectory in state space, are commonly studied in two-level
systems. Here, however, we studythe adiabatic geometric phase in a weakly
anharmonic and strongly driven multi-level system, realised as a
superconducting transmon-type circuit. We measure the contribution of the
second excited state to the two-level geometric phase and find good agreement
with theory treating higher energy levels perturbatively. By changing the
evolution time, we confirm the independence of the geometric phase of time and
explore the validity of the adiabatic approximation at the transition to the
non-adiabatic regime.