arXiv subjects

Yeqing Zhou

Publications and source records attributed to Yeqing Zhou.

4 recordsLinked to original sources

arXiv2024

Exploiting many-body localization for scalable variational quantum simulation

Variational quantum algorithms (VQAs) represent a promising pathway toward achieving practical quantum advantage on near-term hardware. Despite this promise, for generic, expressive ans\"atze, their scalability is critically hindered by barren plateaus--regimes of exponentially vanishing gradients. We demonstrate that initializing a hardware-efficient, Floquet-structured ansatz within the many-body localized (MBL) phase mitigates barren plateaus and enhances algorithmic trainability. Through analysis of the inverse participation ratio, entanglement entropy, and a novel low-weight stabilizer R\'enyi entropy, we characterize a distinct MBL-thermalization transition. Below a critical kick strength, the circuit avoids forming a unitary 2-design, exhibits robust area-law entanglement, and maintains non-vanishing gradients. Leveraging this MBL regime facilitates the efficient variational preparation of ground states for several model Hamiltonians with significantly reduced computational resources. Crucially, experiments on a 127-qubit superconducting processor provide evidence for the preservation of trainable gradients in the MBL phase for a kicked Heisenberg chain, validating our approach on contemporary noisy hardware. Our findings position MBL-based initialization as a viable strategy for developing scalable VQAs and motivate broader integration of localization into quantum algorithm design.

quant-ph↗

arXiv2024

Reducing multivariate independence testing to two bivariate means comparisons

Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear relationships. To explore the reasons behind this issue, we novelly transform the multivariate independence testing problem equivalently into checking the equality of two bivariate means. An important observation we made is that the power loss is mainly due to cancellation of positive and negative terms in dependence metrics, making them very close to zero. Motivated by this observation, we propose a class of consistent metrics with a positive integer $γ$ that exactly characterize independence. Theoretically, we show that the metrics with even and infinity $γ$ can effectively avoid the cancellation, and have high powers under the alternatives that two mean differences offset each other. Since we target at a wide range of dependence scenarios in practice, we further suggest to combine the p-values of test statistics with different $γ$'s through the Fisher's method. We illustrate the advantages of our proposed tests through extensive numerical studies.

stat.ME↗

arXiv2022

On High dimensional Poisson models with measurement error: hypothesis testing for nonlinear nonconvex optimization

We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a non-convex target function to minimize. Treating the high dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive the L1 and L2 convergence rates of the estimator and prove the variable selection consistency. We further establish the asymptotic normality of any subset of the parameters, where the subset can have infinitely many components as long as its cardinality grows sufficiently slow. We develop Wald and score tests based on the asymptotic normality of the estimator, which permits testing of linear functions of the members if the subset. We examine the finite sample performance of the proposed tests by extensive simulation. Finally, the proposed method is successfully applied to the Alzheimer's Disease Neuroimaging Initiative study, which motivated this work initially.

math.ST↗

arXiv2018

Model-Free Conditional Feature Screening with Exposure Variables

In high dimensional analysis, effects of explanatory variables on responses sometimes rely on certain exposure variables, such as time or environmental factors. In this paper, to characterize the importance of each predictor, we utilize its conditional correlation given exposure variables with the empirical distribution function of response. A model-free conditional screening method is subsequently advocated based on this idea, aiming to identify significant predictors whose effects may vary with the exposure variables. The proposed screening procedure is applicable to any model form, including that with heteroscedasticity where the variance component may also vary with exposure variables. It is also robust to extreme values or outlier. Under some mild conditions, we establish the desirable sure screening and the ranking consistency properties of the screening method. The finite sample performances are illustrated by simulation studies and an application to the breast cancer dataset.

stat.ME↗