In this lectures, we have described some essential features of loss of coherence by a qubit coupled to the environment. We have first presented well known semiclassical arguments that relate both decoherence and relaxation to the environmental noise. Then we have shown that models with pure decoherence (but no relaxation in qubit states) can be exactly solvable. As an example, we have treated in detail the model of fluctuating background charges which is believed to describe one of the most important channels for decoherence for the charge Josephson junction qubit. We have shown that the decoherence rate saturates at `high' temperatures while becoming linear in T at low temperatures and showing in all regimes a non-monotonic behaviour as a function of the coupling of the qubit to the fluctuating background charges. We have also considered, albeit only perturbatively, the qubit relaxation by the background charges and demonstrated that a quasi-linear behaviour of the spectral density of noise deduced from the measurements of the relaxation rate can be qualitatively explained.
The performance of various superconducting devices operating at ultra-low temperatures is impaired by the presence of non-equilibrium quasiparticles. Inelastic quasiparticle (QP) tunneling across Josephson junctions in superconducting qubits results in decoherence and spurious excitations and, notably, can trigger correlated errors that severely impede quantum error correction. In this work, we use "gap engineering" to suppress the tunneling of low-energy quasiparticles in Al-based transmon qubits, a leading building block for superconducting quantum processors. By implementing potential barriers for QP, we strongly suppress QP tunneling across the junction and preserve charge parity for over
103 seconds. The suppression of QP tunneling also results in a reduction in the qubit energy relaxation rates. The demonstrated approach to gap engineering can be easily implemented in all Al-based circuits with Josephson junctions.
We investigated decoherence of a Josephson vortex quantum bit (qubit) in dissipative and noisy environment. As the Josephson vortex qubit (JVQ) is fabricated by using a long Josephson junction (LJJ), we use the perturbed sine-Gordon equation to describe the phase dynamics representing a two-state system and estimate the effects of quasiparticle dissipation and weakly fluctuating critical and bias currents on the relaxation time
T1 and on the dephasing time ${T}_{\ensuremath{\phi}}$. We show that the critical current fluctuation does not contribute to dephasing of the qubit in the lowest order approximation. Modeling the weak current variation from magnetic field fluctuations in the LJJ by using the Gaussian colored noise with long correlation time, we show that the coherence time
T2 is limited by the low frequency current noise at very low temperatures. Also, we show that a ultra-long coherence time may be obtained from the JVQ by using experimentally accessible value of physical parameters.