Decoherence in solid-state qubits

The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.     

Remanent quantum correlations in dissipative qubits

Starting from the exact evolution of a Markovian dissipative quantum walk, a non-Markovian decoherence of two qubits interacting with a phonon thermal bath has been investigated analytically using quantum information tools. Concurrence and quantum discord are affected in a complex way, showing that entanglement decreases with dissipation. At the limit where dissipation dominates, quantum correlations survive in time as ∝t^−1/2$\propto t^{-1/2}$. Thus, even under the influence of dissipation, two qubits retain their quantumness for a long time. Quantum correlations could be therefore observed for a long time in related photonic experiments.     

Interfacing quantum-optical and solid-state qubits

We present a generic model of coupling quantum-optical and solid-state qubits, and the corresponding transfer protocols. The example discussed is a trapped ion coupled to a charge qubit (e.g., Cooper pair box). To enhance the coupling and to achieve compatibility between the different experimental setups we introduce a superconducting cavity as the connecting element.     

Dephasing of solid-state qubits at optimal points

Motivated by recent experiments with Josephson-junction circuits, we analyze the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We study the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. For 1/f noise strong higher-order effects influence the evolution.     

Weak values and the Leggett-Garg inequality in solid-state qubits

An implementation of weak values is investigated in solid-state qubits. We demonstrate that a weak value can be nonclassical if and only if a Leggett-Garg inequality can also be violated. Generalized weak values are described in which post-selection occurs on a range of weak measurement results. Imposing classical weak values permits the derivation of Leggett-Garg inequalities for bounded operators. Our analysis is presented in terms of kicked quantum nondemolition measurements on a quantum double-dot charge qubit.     

Indirect interaction of solid-state qubits via two-dimensional electron gas

We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.     

Power injected in dissipative systems and the fluctuation theorem

We consider three examples of dissipative dynamical systems involving many degrees of freedom, driven far from equilibrium by a constant or time dependent forcing. We study the statistical properties of the injected and dissipated power as well as the fluctuations of the total energy of these systems. The three systems under consideration are: a shell model of turbulence, a gas of hard spheres colliding inelastically and excited by a vibrating piston, and a Burridge-Knopoff spring-block model. Although they involve different types of forcing and dissipation, we show that the statistics of the injected power obey the “fluctuation theorem" demonstrated in the case of time reversible dissipative systems maintained at constant total energy, or in the case of some stochastic processes. Although this may be only a consequence of the theory of large deviations, this allows a possible definition of “temperature" for a dissipative system out of equilibrium. We consider how this “temperature" scales with the energy and the number of degrees of freedom in the different systems under consideration. Received 26 June 2000 and Received in final form 24 October 2000     

耗散介观电容耦合电路的量子涨落

给出耗散介观电容耦合电路的量子化,在此基础上研究电荷和电流在能量本征态下的量子涨落,并对其进行讨论 关键词： 耗散电容耦合电路 量子涨落     

Entanglement death and teleportation pre-emption in a dissipative system of two coupled qubits

We discuss the entanglement of two coupled qubits each of which is interacting with a multi-mode squeezed vacuum field reservoir and the possibility to use them in a teleportation protocol. The entanglement sudden death (ESD) and teleportation pre-emption (TPE) are discovered in this system. We consider the interplay between the coupling strength and the squeezing parameter, and find that they play competing roles in entanglement as well as in teleportation. We show in detail how the entanglement decay affects the teleportation. It is interesting to show that TPE precedes ESD in general, and for given measurement result and squeeze parameter all output states of teleportation for a long time arrive at a fixed asymptotic point in the Bloch sphere.     

Density fluctuation spectrum in whistler turbulence

We develop a nonlinear two-dimensional fluid model of whistler turbulence that includes effect of electron fluid density perturbations. The latter is coupled nonlinearly with wave magnetic field. This coupling leads essentially to finite compressibility effects in whistler turbulence model. We find from our simulations that despite strong compressibility effects, the density fluctuations follow the evolution of the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the coupled density fluctuations are found to follow a Kolmogorov-like phenomenology in the inertial range turbulence. Consequently, the turbulent energy is dominated by the large scale (compared to electron inertial length) eddies and it follows a Kolmogorov-like k−7/3 spectrum, where k is a characteristic wavenumber.     

A short and efficient error correcting code for polarization coded photonic qubits in a dissipative channel

We propose a short and efficient non-degenerate quantum error correcting code that is adapted for qubits encoded on two orthogonal, single-photon states (e.g., horizontally and vertically polarized) subject to a dissipative channel.The proposed code draws its strength from the fact that it is adapted to the physical characteristics of the information-carrying basis states under the action of the channel. The code combines different energy manifolds and consists of only 3 spatio-temporal modes and on average 2 photons per code word.     

Shot noise spectrum of open dissipative quantum two-level systems

We study the current noise spectrum of qubits under transport conditions in a dissipative bosonic environment. We combine (non-)Markovian master equations with correlation functions in Laplace space to derive a noise formula for both weak and strong coupling to the bath. The coherence-induced reduction of noise is diminished by weak dissipation and/or a large level separation (bias). For weak dissipation, we demonstrate that the dephasing and relaxation rates of the two-level systems can be extracted from noise. In the strong dissipation regime, the localization-delocalization transition becomes visible in the low-frequency noise.     

Power spectrum of fluctuation for ultrasonic cavitation process in glycerin

Experiments were carried out on ultrasonic cavitation in glycerin. The zone near the emitter has a structure from interacting gas-vapor bubbles; this structure takes the form of fractal clusters. The photometry of passed laser emission was the tool for studying dynamics of fluctuations. In transitive mode, the power spectrum of fluctuation varies by the law inversely proportional to frequency. Distributions of local fluctuations are different from Gaussian and exhibit the property of scale invariance. The qualitative behavior of the frequency dependence of the spectral fluctuation density was tested while varying the power of the ultrasonic emitter. It was demonstrated that the growth of the high-frequency margin of flicker-type behavior evidences for growing instability and can be considered as a forerunner of possible large-scale outbursts. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 05-08-01320a).     

Producing cluster states in charge qubits and flux qubits

We propose a method to efficiently generate cluster states in charge qubits, both semiconducting and superconducting, as well as flux qubits. We show that highly entangled cluster states can be realized by a "one-touch" entanglement operation by tuning gate bias voltages for charge qubits. We also investigate the robustness of these cluster states for nonuniform qubits, which are unavoidable in solid-state systems. We find that quantum computation based on cluster states is a promising approach for solid-state qubits.     

Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wave number ranges in a Beta > or approximately = 1 plasma. The k(-5/3) inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfvén speed. At smaller wavelengths krho(i) > or = 1 the electric spectrum is enhanced and is consistent with the expected dispersion relation of short-wavelength kinetic Alfvén waves. Kinetic Alfvén waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluidlike nature of the solar wind.     

湍流边界层压力起伏频谱特性研究

本工作对水中回转体TBL(湍流边界展)压力起伏频谱特性进行了分析研究.将TBL压力起伏谱分频率高于迁移频率f₀和低于f₀的两个频段描述,给出与实验用模型相应的f₀计算关系;由实验结果的分析得到TBL转捩区和发展区压力起伏频谱与频率、速度间的关系。     

Order parameter fluctuation spectrum and central peak in partially deuterated H-bonded ferroelectrics

The order parameter fluctuation spectrum in an isotopically disordered KH₂PO₄ type crystal has been evaluated as a function of the deuterium content using Mori's continued fraction representation. In contrast to a pure system we have now two narrow central peaks and two overdamped soft modes. The results show that the static central peak observed by light scattering in paraelectric KH₂PO₄ cannot be produced by naturally abundant deuterium.