Topological dynamical decoupling

Science China Physics, Mechanics & Astronomy - Active galactic nuclei (AGNs) have been attracting research attention due to their special observable properties. Specifically, a majority of AGNs...     

Topological dynamical decoupling

We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings,which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application,it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes.     

Fault-tolerant quantum dynamical decoupling

Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. Here we introduce a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors. This is important for coherent control of quantum systems such as quantum computers. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, we show that it is strictly advantageous to use concatenated pulses, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault tolerant and superpolynomially more efficient, at equal cost. We derive a condition on the pulse noise level below which concatenation is guaranteed to reduce decoherence.     

Stochastic oscillations induced by colored noise

We investigate the effect of additive colored noise on Hopf-bifurcating systems in the limit of small correlation times. It is shown that it results in an advancement of the oscillating regime. Several examples are studied.     

Controlling quantum systems by embedded dynamical decoupling schemes

A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired perturbations of quantum systems significantly even for long interaction times. As a first application the stabilization of a quantum memory is discussed which is perturbed by one- and two-qubit interactions.     

A new method of analysis of the effect of weak colored noise in nonlinear dynamical systems

A systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed. It is based on the search of WKB solutions to the Fokker-Planck equation for the joint probability density of the system and noise, in which the perturbation expansion is continued to the first correction beyond the Hamilton-Jacobi limit. The method can be applied to noise with correlation time of order unity. It is illustrated on the normal form of a pitchfork bifurcation, where it is pointed out that additive noise can induce a shift of the most probable value. This prediction is confirmed by numerical simulation of the stochastic differential equations.     

Measuring AFM cantilever stiffness from a thermal noise spectrum

The problem of AFM cantilever calibration from a thermal noise spectrum is considered. A large volume of preliminary work is required to use this method, along with consideration of numerous factors. Use of a synchronous detector allowed us to reduce the requirements for the measuring system and increase the accuracy of spring constant measurement. The respective experimental results are presented.     

Symmetry breakdown of stochastic potential by noise cross-correlations among colored noise sources

A nontrivial phenomenon in stochastic zero-dimensional systems, namely, the symmetry breakdown of stationary probability function due to the correlation between the noises is studied. As a model system to study this effect, we consider a generalized synergetic system of Lorenz type with Gaussian colored noise of each mode. In the frameworks of theoretical approximation and numerical simulations it is shown the fluctuation cross-correlations break the symmetry of bistable synergetic potential, producing an asymmetric effective potential. At that, cross-correlations play the twofold role: cross-correlations are the reason of symmetry breaking at small cross-correlation times on the one hand, and the reason of symmetry restoring at large values of cross-correlation times on the other hand. Moreover, it is shown that symmetry breakdown occurs only if one of multiplicative function is odd. Any other combinations of noises restore the symmetric form of potential.     

Scaling of dynamical decoupling for spin qubits

We investigate the scaling of coherence time T(2) with the number of π pulses n(π) in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law T(2) is proportional to (n(π))(γ(e)), with γ(e)=0.72±0.01, essentially independent of the envelope function used to extract T(2). From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(ω)~ω(-β), yields β=γ(e)/(1-γ(e))=2.6±0.1. Model values for T(2)(n(π)) using β=2.6 for CPMG with both even and odd n(π) up to 32 and CDD orders 3 through 6 compare very well with the experiment.     

Identifying the interactions in a colored dynamical network

The interactions of a colored dynamical network play a great role in its dynamical behaviour and are denoted by outer and inner coupling matrices. In this paper, the outer and inner coupling matrices are assumed to be unknown and need to be identified. A corresponding network estimator is designed for identifying the unknown interactions by adopting proper adaptive laws. Based on the Lyapunov function method and Barbalat's lemma, the obtained result is analytically proved. A colored network coupled with chaotic Lorenz, Chen, and L systems is considered as a numerical example to illustrate the effectiveness of the proposed method.     

Use of decoupling to reduce the radiated noise generated by panels

Four types of sources that induce on a panel four different responses are considered. The differences show up also in the way the responses radiate to the far field. A decoupling device in a form of a layer is placed adjacent to the top surface of the panel. The decoupling layer modifies the radiated fields that the sources generate. The modifications in terms of radiation reduction factors and levels are defined. These factors and levels are analyzed for two kinds of decoupling layers. The first is a compliant coating and the second is a layer of a mixture of gas and fluid. The compliant coating may induce on the fluid a velocity field that is different from that of the panel. The mixture of gas and fluid introduces a surface impedance discontinuity between the top surface of the panel and the top surface of the layer, the top surface being in contact with the semi-infinite fluid above the panel.     

Langevin-like equation with colored noise

Consider a stochastic differential equation of the form of a Langevin equation, but in which the noise source is not white. If it is nearly white, i.e., its autocorrelation time is short, a systematic approximation method is known. It leads to a Fokker-Planck equation with successive higher order corrections. To obtain the coefficients more explicitly, a secondary expansion may be employed. The validity of the resulting double series approximation is discussed and confronted with the various results given in the literature. In addition, an alternative approximation method is obtained using the technique for eliminating fast variables. It produces the same terms in a different sequence.     

Suppressing noises with topology and dynamical decoupling

<正>High-quality qubits are essential components of practical quantum computers. However, physical qubits inevitably interact with their environments, which causes decoherence and dissipation. To overcome this problem, one may employ an approach to isolate the qubits from their environments. Dynamical decoupling is a strong candidate, and it protects qubits by repeatedly applying some operations to average out the unwanted interactions.     

High fidelity quantum gates via dynamical decoupling

Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of magnitude improvement in the fidelities of a universal set of quantum gates, relative to unprotected evolution, is achieved over a broad range of system-environment coupling strengths, using recursively constructed (concatenated) dynamical decoupling pulse sequences.     

Stochastic resonance in periodic potentials driven by colored noise

We studied the motion of an underdamped Brownian particle in a periodic potential subject to a harmonic excitation and a colored noise. The average input energy per period and the phase lag are calculated to quantify the phenomenon of stochastic resonance (SR). The numerical results show that most of the out-of-phase trajectories make a transition to the in-phase state as the temperature increases. And the colored noise delays the transitions between these two dynamical states. The each curve of the average input energy per period and the phase lag versus the temperature exist a mono peak and SR appears in this system. Moreover, the optimal temperature where the SR occurs becomes larger and the region of SR grows wider as the correlation time of colored noise increases.     

Stabilization of quantum information by combined dynamical decoupling and detected-jump error correction

Two possible applications of random decoupling are discussed. Whereas so far decoupling methods have been considered merely for quantum memories, here it is demonstrated that random decoupling is also a convenient tool for stabilizing quantum algorithms. Furthermore, a decoupling scheme is presented which involves a random decoupling method compatible with detected-jump error correcting quantum codes. With this combined error correcting strategy it is possible to stabilize quantum information against both spontaneous decay and static imperfections of a qubit-based quantum information processor in an efficient way.