BURA Collection:http://bura.brunel.ac.uk/handle/2438/86282024-03-16T19:17:17Z2024-03-16T19:17:17ZEfficient classical simulation of cluster state quantum circuits with alternative inputsAtallah, SGarn, MJevtic, STao, YVirmani, Shttp://bura.brunel.ac.uk/handle/2438/284052024-02-26T03:01:02Z2024-02-06T00:00:00ZTitle: Efficient classical simulation of cluster state quantum circuits with alternative inputs
Authors: Atallah, S; Garn, M; Jevtic, S; Tao, Y; Virmani, S
Abstract: We provide new examples of pure entangled systems related to cluster state quantum computation that can be efficiently simulated classically. In cluster state quantum computation input qubits are initialised in the `equator' of the Bloch sphere, CZ gates are applied, and finally the qubits are measured adaptively using Z measurements or measurements of cos(θ)X + sin(θ)Y operators. We consider what happens when the initialisation step is modified, and show that for lattices of finite degree D, there is a constant λ ≈ 2.06 such that if the qubits are prepared in a state that is within λ^−D in trace distance of a state that is diagonal in the computational basis, then the system can be efficiently simulated classically in the sense of sampling from the output distribution within a desired total variation distance. In the square lattice with D = 4 for instance, λ ^−D ≈ 0.056. We develop a coarse grained version of the argument which increases the size of the classically efficient region. In the case of the square lattice of qubits, the size of the classically simulatable region increases in size to at least around ≈ 0.070, and in fact probably increases to around ≈ 0.1. The results generalise to a broader family of systems, including qudit systems where the interaction is diagonal in the computational basis and the measurements are either in the computational basis or unbiased to it. Potential readers who only want the short version can get much of the intuition from figures 1 to 3.2024-02-06T00:00:00ZRenewable Huber estimation method for streaming datasetsJiang, RLiang, L.Yu, Khttp://bura.brunel.ac.uk/handle/2438/283262024-03-10T18:30:19Z2024-02-23T00:00:00ZTitle: Renewable Huber estimation method for streaming datasets
Authors: Jiang, R; Liang, L.; Yu, K
Abstract: Streaming data refers to a data collection scheme where observations arrive sequentially and perpetually over time, making it challenging to fit into computer memory for statistical analysis. The ordinary least squares estimate for linear regression is sensitive to heavy-tailed errors and outliers, which are commonly encountered in applications. In this case, the Huber loss function is a useful criterion for robust regression. In this paper, we propose robust regression estimation and variable selection for streaming datasets. Unlike the renewable estimation generalized linear regression for streaming datasets, however, the Huber loss function is only first-order differentiable, which poses challenges to renewable estimation in both computation and theoretical development. To address the challenge, we introduce a new smoothed version of the Huber first derivative, which admits a fast and scalable algorithm to perform optimization for streaming data sets and achieves the best fitting of Huber function among different versions. Theoretically, the proposed statistics are shown to have the same asymptotic properties as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. The proposed methods are illustrated using current data and the summary statistics of historical data. Both simulations and real data analysis are conducted to illustrate the finite sample performance of the proposed methods.
Description: MSC2020 subject classifications: Primary 60G08; secondary 62G20.2024-02-23T00:00:00ZHigher order asymptotics for large deviations – Part IFernando, KHebbar, Phttp://bura.brunel.ac.uk/handle/2438/278662023-12-17T03:00:58Z2021-02-03T00:00:00ZTitle: Higher order asymptotics for large deviations – Part I
Authors: Fernando, K; Hebbar, P
Abstract: For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth Expansions for the Central Limit Theorem. We show that the results are applicable to Diophantine iid sequences, finite state Markov chains, strongly ergodic Markov chains and Birkhoff sums of smooth expanding maps & subshifts of finite type.
Description: The file archived on this institutional repository is a preprint available online at https://arxiv.org/abs/1811.06793. It has not been certified by peer review. Please consult the version of record available published by IOS Press at https://doi.org/10.3233/ASY-201602 .2021-02-03T00:00:00ZEdgeworth expansions for weakly dependent random variablesFernando, KLiverani, Chttp://bura.brunel.ac.uk/handle/2438/278652023-12-16T03:01:06Z2021-02-01T00:00:00ZTitle: Edgeworth expansions for weakly dependent random variables
Authors: Fernando, K; Liverani, C
Abstract: We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the CLT for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like piece-wise expanding maps, and strongly ergodic Markov chains. As a corollary we obtain refinements of the Local Limit Theorem and moderate deviation results. We primarily use spectral techniques to obtain the results.
Nous discutons des conditions suffisantes garantissant l’existence d’expansions asymptotiques du théorème central limite pour des variables aléatoires faiblement dépendantes, dont des observations provenant de systèmes dynamiques suffisamment chaotiques comme des applications dilatantes par morceaux, et des chaînes de Markov fortement ergodiques. Comme corollaire, nous obtenons des raffinements du théorème local limite et de résultats de déviations modérées. Nos méthodes sont principalement des techniques spectrales.2021-02-01T00:00:00Z