We propose and study a model of dephasing due to an environment of bistable fluctuators. We apply our analysis to the decoherence of Josephson qubits, induced by background charges present in the substrate, which are also responsible for the 1/f noise. The discrete nature of the environment leads to a number of new features which are mostly pronounced for slowly moving charges. Far away from the degeneracy this model for the dephasing is solved exactly.
We propose and study a model of dephasing due to an environment of bistable fluctuators. We apply our analysis to the decoherence of Josephson qubits, induced by background charges present in the substrate, which are also responsible for the 1/f noise. The discrete nature of the environment leads to a number of new features which are mostly pronounced for slowly moving charges. Far away from the degeneracy this model for the dephasing is solved exactly.
A high degree of quantum coherence is a crucial requirement for the implementation of quantum logic devices. Solid state nanodevices seem particularly promising from the point of view of integrability and flexibility in the design. However decoherence is a serious limitation, due to the presence of many types low energy excitations in the ``internal'' environment and of ``external'' sources due to the control circuitery. Here we study both kind of dephasing in a special implementation, the charge Josephson qubit, however many of our results are applicable to a large class of solid state qubits. This is the case of 1/f noise for which we introduce and study a model of an environment of bistable fluctuatiors. External sources of noise are analized in terms of a suitable harmonic oscillator environment and the explicit mapping on the spin boson model is presented. We perform a detailed investigation of various computation procedures (single shot measurements, repeated measurements) and discuss the problem of the information needed to characterize the effect of the environment. For a fluctuator environment with 1/f spectrum memory effects turn out to be important. Although in general information beyond the power spectrum is needed, in many situations this results in the knowledge of only one more microscopic parameter of the environment. This allows to determine which degrees of freedom of the environment are effective sources of decoherence in each different physical situation considered.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. 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. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
Motivated by recent experiments with Josephson qubits we propose a new phenomenological model for 1/f noise due to collective excitations of interacting defects in the qubit's environment. At very low temperatures the effective dynamics of these collective modes are very slow leading to pronounced non-Gaussian features and nonstationarity of the noise. We analyze the influence of this noise on the dynamics of a qubit in various regimes and at different operation points. Remarkable predictions are absolute time dependences of a critical coupling and of dephasing in the strong coupling regime.
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.
We theoretically study the dephasing of an Andreev spin qubit (ASQ) due to electric and magnetic noise. Using a tight-binding model, we calculate the Andreev states formed in a Josephson junction where the link is a semiconductor with strong spin-orbit interaction. As a result of both the spin-orbit interaction and induced superconductivity, the local charge and spin of these states vary as a function of externally controllable parameters: the phase difference between the superconducting leads, an applied magnetic field, and filling of the underlying semiconductor. Concomitantly, coupling to fluctuations of the electric or magnetic environment will vary, which informs the rate of dephasing. We qualitatively predict the dependence of dephasing on the nature of the environment, magnetic field, phase difference between the junction, and filling of the semiconductor. Comparing the simulated electric- and magnetic-noise-induced dephasing rate to experiment suggests that the dominant source of noise is magnetic. Moreover, by appropriately tuning these external parameters, we find sweet spots at which we predict an enhancement in ASQ coherence times.
In quantum computation, quantum coherence must be maintained during gate operation. However, in physical implementations, various couplings with the environment are unavoidable and can lead to a dephasing of a quantum bit (qubit). The background charge fluctuations are an important dephasing process, especially in a charge qubit system. We examined the dephasing rate of a qubit due to random telegraph noise. Solving stochastic differential equations, we obtained the dephasing rate of a qubit constructed of a coupled-dot system; we applied our results to the charge Josephson qubit system. We examined the dephasing rates due to two types of couplings between the coupled-dot system and the background charge, namely, fluctuation in the tunnel coupling constant and fluctuation in the asymmetric bias. For a strong-coupling condition, the dephasing rate was inversely proportional to the time constant of the telegraph noise. When there is fluctuation in the tunnel coupling constant, Gaussian decay occurs in the initial regime. We also examined the rate of dephasing due to many impurity sites. For a weak-coupling condition with fluctuation in the asymmetric bias, the obtained dephasing rate coincided with that obtained by the perturbation method using the spectral weight of a boson thermal bath, which is proportional to the inverse of the frequency.