The efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the individual qubits and quantum gates. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources obtained by engineering. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, quantum devices are affected by noise decreasing with frequency $f$ approximately as $1/f$. According to the present point of view, such noise is due to material- and device-specific microscopic degrees of freedom interacting with quantum variables of the nanodevice. The simplest picture is that the environment that destroys the phase coherence of the device can be thought of as a system of two-state fluctuators, which experience random hops between their states. If the hopping times are distributed in an exponentially broad domain, the resulting fluctuations have a spectrum close to $1/f$ in a large frequency range. This paper reviews the current state of the theory of decoherence due to degrees of freedom producing $1/f$ noise. Basic mechanisms of such noises in various nanodevices are discussed and several models describing the interaction of the noise sources with quantum devices are reviewed. The main focus of the review is to analyze how the $1/f$ noise destroys their coherent operation. The start is from individual qubits concentrating mostly on the devices based on superconductor circuits and then some special issues related to more complicated architectures are discussed. Finally, several strategies for minimizing the noise-induced decoherence are considered.

We study decoherence in a qubit with the distance between the two levels affected by random flips of bistable fluctuators. For the case of a single fluctuator we evaluate explicitly an exact expression for the phase-memory decay in the echo experiment with a resonant ac excitation. The echo signal as a function of time shows a sequence of plateaus. The position and the height of the plateaus can be used to extract the fluctuator switching rate $\gamma$ and its coupling strength $v$. At small times the logarithm of the echo signal is $\propto t^3$. The plateaus disappear when the decoherence is induced by many fluctuators. In this case the echo signal depends on the distribution of the fluctuators parameters. According to our analysis, the results significantly deviate from those obtained in the Gaussian model as soon as $v\gtrsim \gamma$.

Recent theoretical analysis of spatially-nonuniform modes of the thermomagnetic instability in superconductors [Phys. Rev. B 70, 224502 (2004)] is generalized to the case of a thin film in a perpendicular applied field. We solve the thermal diffusion and Maxwell equations taking into account nonlocal electrodynamics in the film and its thermal coupling to the substrate. The instability is found to develop in a nonuniform, fingering pattern if the background electric field, $E$, is high and the heat transfer coefficient to the substrate, $h_0$, is small. Otherwise, the instability develops in a uniform manner. We find the threshold magnetic field, $H_{\mathrm{fing}}(E,h_0)$, the characteristic finger width, and the instability buildup time. Thin films are found to be much more unstable than bulk superconductors, and have a stronger tendency for formation of fingering (dendritic) pattern.

Recent experiments by Yoshihara et al. [Phys. Rev. Lett. 97, 167001 (2006)] provided information on decoherence of the echo signal in Josephson-junction flux qubits at various bias conditions. These results were interpreted assuming a Gaussian model for the decoherence due to $1∕f$ noise. Here we revisit this problem on the basis of the exactly solvable spin-fluctuator model reproducing detailed properties of the $1∕f$ noise interacting with a qubit. We consider the time dependence of the echo signal and conclude that the results based on the Gaussian assumption need essential reconsideration.

Stability of the vortex matter—magnetic flux lines penetrating into the material—in type-II superconductor films is crucially important for their application. If some vortices get detached from pinning centres, the energy dissipated by their motion will facilitate further depinning, and may trigger an electromagnetic breakdown. In this paper, we review recent theoretical and experimental results on development of the above mentioned thermomagnetic instability. Starting from linear stability analysis for the initial critical-state flux distribution we then discuss a numerical procedure allowing to analyze developed flux avalanches. As an example of this approach we consider ultra-fast dendritic flux avalanches in thin superconducting disks. At the initial stage the flux front corresponding to the dendrite's trunk moves with velocity up to 100 km/s. At later stage the almost constant velocity leads to a specific propagation regime similar to ray optics. We discuss this regime observed in superconducting films coated by normal strips. Finally, we discuss dramatic enhancement of the anisotropy of the flux patterns due to specific dynamics. In this way we demonstrate that the combination of the linear stability analysis with the numerical approach provides an efficient framework for understanding the ultra-fast coupled nonlocal dynamics of electromagnetic fields and dissipation in superconductor films.

Small metal particles embedded in a material subject to an external electric field can contribute to the conductance by mechanically transporting charge. This was already demonstrated in Millikan's pioneering experiment that proved that charge is quantized. While the effect of charge quantization can be pronounced for submicron conducting particles and lead to Coulomb blockade of tunnelling, the nanomechanical aspect of single-electron tunnelling becomes prominent only in nanometer-size self-assembled structures. The coupling between mechanical deformations and electronic charge transport in composite materials with nanoscale components gives rise to a new class of phenomena—nanoelectromechanical transport—and opens up a new route in nanotechnology. The interplay between the electronic and mechanical degrees of freedom is especially important in nanocomposites consisting of materials with very different elastic properties. A typical system of this kind is a single-electron transistor (SET) with deformable tunnel barriers, a so called Nano-Electro-Mechanical SET (NEM-SET). The new kind of electron transport in this and other types of nanodevices is referred to as "shuttle transport" of electrons, which implies that electrons is transferred between metallic leads via a movable small-sized cluster. The present review is devoted to the fundamental aspects of shuttle transport and to a description of major developments in the theoretical and experimental research in the field. Prospective applications of this exciting phenomenon that remarkably combines traditional mechanics of materials with the most advanced effects of quantum physics, will also be touched upon.