Fault-tolerant quantum computation with long-range correlated noise

We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r(D).     

Nonlocal Kardar-Parisi-Zhang equation with spatially correlated noise

The effects of spatially correlated noise on a phenomenological equation equivalent to a nonlocal version of the Kardar-Parisi-Zhang (KPZ) equation are studied via the dynamic renormalization group (DRG) techniques. The correlated noise coupled with the long ranged nature of interactions prove the existence of different phases in different regimes, giving rise to a range of roughness exponents defined by their corresponding critical dimensions. Finally self-consistent mode analysis is employed to compare the non-KPZ exponents obtained as a result of the long-range interactions with the DRG results.     

Improved speech recognition in noise in simulated binaurally combined acoustic and electric stimulation

Speech recognition in noise improves with combined acoustic and electric stimulation compared to electric stimulation alone [Kong et al., J. Acoust. Soc. Am. 117, 1351-1361 (2005)]. Here the contribution of fundamental frequency (F0) and low-frequency phonetic cues to speech recognition in combined hearing was investigated. Normal-hearing listeners heard vocoded speech in one ear and low-pass (LP) filtered speech in the other. Three listening conditions (vocode-alone, LP-alone, combined) were investigated. Target speech (average F0=120 Hz) was mixed with a time-reversed masker (average F0=172 Hz) at three signal-to-noise ratios (SNRs). LP speech aided performance at all SNRs. Low-frequency phonetic cues were then removed by replacing the LP speech with a LP equal-amplitude harmonic complex, frequency and amplitude modulated by the F0 and temporal envelope of voiced segments of the target. The combined hearing advantage disappeared at 10 and 15 dB SNR, but persisted at 5 dB SNR. A similar finding occurred when, additionally, F0 contour cues were removed. These results are consistent with a role for low-frequency phonetic cues, but not with a combination of F0 information between the two ears. The enhanced performance at 5 dB SNR with F0 contour cues absent suggests that voicing or glimpsing cues may be responsible for the combined hearing benefit.     

Superdiffusive conduction: AC conductivity with correlated noise

We present evidence of the existence of a superdiffusive regime in systems with correlated disorder for which localization is suppressed. An expression for anomalous electrical conductivity at low frequencies is found by using a generalized Langevin equation whose memory function accounts for the interactions between the carriers. New mechanisms inducing a superdiffusive conductivity are discussed and experimental possibilities for observing that phenomenon in nanotubes and super-lattices are presented.     

Hedgehog production in spatially correlated noise

The production of topological defects during a quench in a φ⁴ model is investigated. The influence of a spatially correlated noise on defect production in two and three dimensions is demonstrated. Received 28 August 2001 / Received in final form 11 February 2002 Published online 2 October 2002 RID="a" ID="a"Paper supported in part by ESF “COSLAB” Programme RID="b" ID="b"e-mail: sfdobrow@kinga.cyf-kr.edu.pl     

Escape driven by strongly correlated noise

We consider the colored-noise-driven archetypal bistability dynamics of the Ginzburg-Landau type. The focus is on the stationary behavior and the problem of escape from metastable states. The deterministic flow of the underlyingtwo-variable Fokker-Planck process is studied as a function of the noise correlation time . As a main result we find that the separatrix exhibits a cusp at asymptotically large noise color. The stationary probability is evaluated approximately (unified colored noise approximation) and compared with numerical exact results. The stationary probability forms the key input in the evaluation of the rate of escape. At very strong noise color, the escape path closely follows a nodal line, passing through the corresponding stable node. The asymptotic result for the escape rate at large is compared with exact calculations for the lowest, nonvanishing eigenvalue.     

Exact results for the Kardar-Parisi-Zhang equation with spatially correlated noise

We investigate the Kardar-Parisi-Zhang (KPZ) equation in d spatial dimensions with Gaussian spatially long-range correlated noise -- characterized by its second moment -- by means of dynamic field theory and the renormalization group. Using a stochastic Cole-Hopf transformation we derive exact exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension . Below the lower critical dimension, there is a line marking the stability boundary between the short-range and long-range noise fixed points. For , the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above , one has to rely on some perturbational techniques. We discuss the location of this stability boundary in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively. Received 5 August 1998     

Growth in a restricted solid on solid model with correlated noise

We introduce correlated growth into a restricted solid on solid model (RSOS), a stochastic deposition model with a constraint on neighboring height differences. A two-dimensional lattice model is used in which particles are deposited via horizontal Levy flight steps with a step length distribution exponentf. Though RSOS is in the same universality class as ballistic deposition for uncorrelated deposition, it appears to depart from it for strong correlations. Forf=1, the short-range limit is reached and both exponents and, which describe the dependence of surface width on time and strip length, tend to 1. Forf>1 we retreat to an enhanced algorithm, searching for growth sites which become excessively rare. We find an unusual short-time dependence, but still tends to 1. The number of growth sitesG shows saturation forf<1, while forf1 we observeG/L0 as the strip lengthL increases. Finally, we test directly the relationship of noise-noise correlation strength tof, and find that a direct comparison between correlated growth models and theoretical predictions for growth with correlated noise is so far unjustified.     

Decoherence by correlated noise and quantum error correction

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.     

Quantum error correction in spatially correlated quantum noise

We consider quantum error correction of quantum noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kinds of noise correlations have a strong negative impact on quantum error correction.     

含关联噪声的空间分数阶随机生长方程的动力学标度行为研究

为探讨含关联噪声的空间分数阶随机生长方程的动力学标度行为,本文利用Riesz分数阶导数和Grümwald-Letnikov分数阶导数定义方法研究了关联噪声驱动下的空间分数阶Edwards-Wilkinson (SFEW)方程在1+1维情况下的数值解,得到了不同噪声关联因子和分数阶数时的生长指数、粗糙度指数、动力学指数等,所求出的临界指数均与标度分析方法的结果相符合.研究表明噪声关联因子和分数阶数均影响到SFEW方程的动力学标度行为,且表现为连续变化的普适类.     

含时空关联噪声生长方程的标度奇异性分析

基于动力学重整化群理论研究表面界面生长动力学标度奇异性问题, 得到含时空关联噪声的表面生长方程标度奇异指数的一般结果,并将此方法应用于几种典型的局域生长方程——Kardar-Parisi-Zhang（KPZ）方程、线性生长方程、Lai-Das Sarma-Villain（LDV）方程.结果表明,在长波长极限下局域生长方程的动力学标度奇异性与最相关项、基底维数以及噪声有关,并且若出现标度奇异性,只会是超粗化（super rough）奇异标度行为,而不是内禀（intrinsically）奇异标度行为. 关键词： 标度奇异性 动力学重整化群理论 时空关联噪声     

空间关联白噪声影响下小世界神经元网络系统的同步动力学

以电耦合的Terman-Wang小世界神经元网络系统为研究对象, 研究了空间关联白噪声影响下神经元网络系统的同步动力学. 首先将动力学平均场近似理论扩展到受空间关联白噪声影响下的小世界网络系统中, 将描述网络系统动力学演化的2N维随机微分方程简化为11个确定性的矩微分方程. 其次, 基于动力学平均场近似理论所推导的矩方程, 讨论了空间关联噪声、网络结构参数对神经元网络系统同步动力学的关键影响, 发现较大的噪声空间关联系数、耦合强度及节点平均度均对神经元网络系统同步放电具有积极作用. 进一步地, 利用计算机仿真数值模拟原神经元网络系统的同步动力学, 并与基于动力学平均场近似理论所得到的结果进行比较, 发现二者具有较好的一致性.     

Bistability driven by correlated noise: Functional integral treatment

A complete study of non-Markovian effects induced by correlated noise applied to a bistable dynamical system is presented. Starting from the exact functional integral solution of the stochastic equation, it is possible to show that the customary expansion in powers of the characteristic correlation time gives wrong asymptotic results. Other approaches based on a Fokker-Planck equation with a modified diffusion coefficient also fail in reproducing the right long-time behavior of the system. Using a generalized version of instanton calculus of functional integrals, explicit expressions of the invariant measure and transition time between stable fixed points are obtained, in the limit of small noise intensity but arbitrary correlation time. In particular, an original method for extracting the collective degrees of motion has been developed. These analytical results fit, for a large range of parameters, with numerical calculations, giving confidence in the formalism employed.     

Surrogate analysis of volatility series from long-range correlated noise

Detrended fluctuation analysis (DFA) [C.-K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, F. Sciortino, M. Simons, H.E. Stanley, Nature 356 (1992) 168] of volatility series has been proposed to identify possible nonlinear/multifractal signatures in the given empirical sample [Y. Ashkenazy, P.Ch. Ivanov, S. Havlin, C.-K. Peng, A.L. Goldberger, H.E. Stanley, Phys. Rev. Lett. 86 (2001) 1900; Y. Ashkenazy, S. Havlin, P. Ch. Ivanov, C.-K. Peng, V. Schulte-Frohlinde, H.E. Stanley, Physica A. 323 (2003) 19; T. Kalisky, Y. Ashkenazy, S. Havlin, Phys. Rev. E 72 (2005) 011913]. Long-range volatility correlation can be an outcome of static as well as dynamical nonlinearity. In order to argue in favor of dynamical nonlinearity, surrogate testing is used in conjunction with volatility analysis [Y. Ashkenazy, P.Ch. Ivanov, S. Havlin, C.-K. Peng, A.L. Goldberger, H.E. Stanley, Phys. Rev. Lett. 86 (2001) 1900; Y. Ashkenazy, S. Havlin, P. Ch. Ivanov, C.-K. Peng, V. Schulte-Frohlinde, H.E. Stanley, Physica A. 323 (2003) 19; T. Kalisky, Y. Ashkenazy, S. Havlin, Phys. Rev. E 72 (2005) 011913]. In this brief communication, surrogate testing of volatility series from long-range correlated monofractal noise and their static, invertible nonlinear transforms is investigated. Long-range correlated noise is generated from fractional auto regressive integrated moving average (FARIMA) (0, d, 0), with Gaussian and non-Gaussian innovations. We show significant deviation in the scaling behavior between the empirical sample and the surrogate counterpart at large time-scales in the case of FARIMA (0, d, 0) with non-Gaussian innovations whereas no such discrepancy was observed in the case of Gaussian innovations. The results encourage cautious interpretation of surrogate analysis of volatility series in the presence of non-Gaussian innovations.     

Single-channel speech enhancement method using reconstructive NMF with spectrotemporal speech presence probabilities

In this paper, a novel single microphone channel-based speech enhancement technique is presented. While most of the conventional nonnegative matrix factorization-based approaches focus on generating a basis matrix of speech and noise for enhancement, the proposed algorithm performs an additional process to reconstruct speech from noisy speech when these two elements are highly overlapped in selected spectral bands. This process involves a log-spectral amplitude based estimator, which provides the spectrotemporal speech presence probability to obtain a more accurate reconstruction. Moreover, the proposed algorithm applies an unsupervised learning method to the input noise, so it is adaptable to any type of environmental noise without a pre-trained dictionary. The experimental results demonstrate that the proposed algorithm obtains improved speech enhancement performance compared with conventional single channel-based approaches.     

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加.