Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties.

We have considered the quantum dynamics of an array of nSQUIDs -two-junction SQUIDs with negative mutual inductance between their two arms. Effective dual-rail structure of the array creates additional internal degree of freedom for the fluxons in the array, which can be used to encode and transport quantum information. Physically, this degree of freedom is represented by electromagnetic excitations localized on the fluxon. We have calculated the spatial profile and frequency spectrum of these excitations. Their dynamics can be reduced to two quantum states, so that each fluxons moving through the array carries with it a qubit of information. Coherence properties of such a propagating qubits in the nSQUID array are characterized by the dynamic suppression of the lowfrequency decoherence due to the motion-induced spreading of the noise spectral density to a larger frequency interval.