arXiv subjects

Zhichun Yang

Publications and source records attributed to Zhichun Yang.

7 recordsLinked to original sources

arXiv2026

An error bound-based convergence analysis framework for a class of randomized algorithms

Classical analyses show that randomized coordinate descent (RCD) and gradient descent (GD) share the same convergence rates in terms of objective gap under convexity and specific global EB-type assumptions. However, this rate preservation phenomenon does not extend to iterate rates, almost-sure rates, or general local error bound conditions. In this paper, we study this phenomenon systematically, not only for RCD but also for a much broader class of algorithms that share the same structures. Specifically, we introduce an abstract class of algorithms, called monotone randomized algorithms (MRAs), and new unified error bound (UEB) conditions that are independent of problem class and accommodate general EB moduli. These UEB conditions subsume many EB- and Kurdyka--\L{}ojasiewicz-type assumptions used in the analysis of algorithms for optimization, convex feasibility, and common fixed point problems. We then develop a new analysis framework and a set of technical tools that yield nonasymptotic in-expectation rates and asymptotic almost-sure rates for both the optimality measure and the iterates under the global UEB condition. Under the local UEB condition, we further establish asymptotic almost-sure rates for both quantities. For comparison, we introduce the monotone deterministic algorithms (MDAs), as the corresponding deterministic counterpart of MRAs. We illustrate the tightness of our MRA analysis by showing that the lower bounds of MDAs match the upper bounds of MRAs qualitatively. We also demonstrate the strength and versatility of our framework through three applications, namely generalized randomized subspace descent for unconstrained minimization, randomized block proximal gradient methods for composite optimization, and the randomized Krasnosel'ski\u{\i}--Mann method for common fixed point problems.

math.OC↗

arXiv2025

Super-bunching light with giant high-order correlations and extreme multi-photon events

Non-classical light sources emitting bundles of N-photons with strong correlation represent versatile resources of interdisciplinary importance with applications ranging from fundamental tests of quantum mechanics to quantum information processing. Yet, high-order correlations, gN(0),quantifying photon correlation, are still limited to hundreds. Here, we report the generation of a super-bunching light source in photonic crystal fiber with g2(0) reaching 5.86*104 and g5(0) up to 2.72*108, through measuring its photon number probability distributions. under giant g2(0) values, the super-bunching light source presents upturned-tail photon distributions and ubiquitous extreme multi-photon events, where 31 photons from a single light pulse at a mean of 1.99*10-4 photons per pulse have been determined. The probability of this extreme event has been enhanced by 10139 folds compared to a coherent laser with Poissonian distribution. By varying the power of the pumping laser, both photon number distributions and corresponding high-order correlations of this light source can be substantially tailored from Poissonian to super-bunching distributions. These phenomena are attributed to the synchronized nonlinear interactions in photonic crystal fibers pumping by bright squeezed light, and the theoretical simulations agree well with the experimental results. Our research showcases the ability to achieve non-classical light sources with giant high-order correlations and extreme multi-photon events, paving the way for high-order correlation imaging, extreme nonlinear optical effects, quantum information processing, and exploring light-matter interactions with multi-photon physics.

quant-ph↗

arXiv2025

Stable self-charged perovskite quantum rods for liquid laser with near-zero threshold

Colloidal quantum dots (QDs) are promising optical gain materials that require further threshold reduction to realize their full potential. While QD charging theoretically reduces the threshold to zero, its effectiveness has been limited by strong Auger recombination and unstable charging. Here we theoretically reveal the optimal combination of charging number and Auger recombination to minimize the lasing threshold. Experimentally, we develop stable self-charged perovskite quantum rods (QRs) as an alternative to QDs via state engineering and Mn-doping strategy. An unprecedented two-order-of-magnitude reduction in nonradiative Auger recombination enables QRs to support a sufficient charging number of up to 6. The QR liquid lasing is then achieved with a near-zero threshold of 0.098 using quasi-continuous pumping of nanosecond pulses, which is the lowest threshold among all reported QD lasers. These achievements demonstrate the potential of the specially engineered QRs as an excellent gain media and pave the way for their prospective applications.

cond-mat.mes-hall↗

arXiv2025

On-demand manipulation of superbunching emission from colloidal quantum dots and its application in noise-resistance correlated biphoton imaging

Superbunching effect with second-order correlations larger than 2, $g^{(2)}(0)>2$, indicating the N-photon bundles emission and strong correlation among photons, has a broad range of fascinating applications in quantum illumination, communication, and computation. However, the on-demand manipulation of the superbunching effect in colloidal quantum dots (QDs) under pulsed excitation, which is beneficial to integrated photonics and lab-on-a-chip quantum devices, is still challenging. Here, we disclosed the evolution of $g^{(2)}(0)$ with the parameters of colloidal QDs by Mento Carlo simulations and performed second-order correlation measurements on CdSe/ZnS core/shell QDs under both continuous wave (CW) and pulsed lasers. The photon statistics of a single colloidal QD have been substantially tailored from sub-Poissonian distribution $g^{(2)}(0) <1$) to superbunching emission, with the maximum $g^{(2)}(0)$ reaching 69 and 20 under CW and pulsed excitation, respectively. We have achieved correlated biphoton imaging (CPI), employing the coincidence of the biexciton and bright exciton in one laser pulse, with the stray light and background noise up to 53 times stronger than PL emission of single colloidal QDs. By modulating the PL intensity, the Fourier-domain CPI with reasonably good contrast has been determined, with the stray light noise up to 107 times stronger than PL emission and 75600 times stronger than the counts of biphotons. Our noise-resistance CPI may enable laboratory-based quantum imaging to be applied to real-world applications with the highly desired suppression of strong background noise and stray light.

physics.optics↗

arXiv2024

Variance Reduced Random Relaxed Projection Method for Constrained Finite-sum Minimization Problems

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to efficiently solve this problem. Compared with existing RPMs, our proposed algorithm features two useful algorithmic ideas. First, at each iteration, instead of projecting onto the subset defined by one of the constraints, our algorithm only requires projecting onto a half-space approximation of the subset, which significantly reduces the computational cost as it admits a closed-form formula. Second, to exploit the structure that the objective is a sum, variance reduction is incorporated into our algorithm to further improve the performance. As theoretical contributions, under a novel error bound condition and other standard assumptions, we prove that the proposed RPM converges to an optimal solution and that both optimality and feasibility gaps vanish at a sublinear rate. In particular, via a new analysis framework, we show that our RPM attains a faster convergence rate in optimality gap than existing RPMs when the objective function has a Lipschitz continuous gradient, capitalizing the benefit of the variance reduction. We also provide sufficient conditions for the error bound condition to hold. Experiments on a beamforming problem and a robust classification problem are also presented to demonstrate the superiority of our RPM over existing ones.

math.OC↗

arXiv2021

Elastic Bound State in the Continuum with Perfect Mode Conversion

The partial or complete confinement of waves in an open system is omnipresent in nature and in wave-based materials and technology. Here, we theoretically analyze and experimentally observe the formation of a trapped mode with perfect mode conversion (TMPC) between flexural waves and longitudinal waves, by achieving a quasi-bound state in the continuum (BIC) in an open elastic wave system. The latter allows a quasi-BIC in a semi-infinite background plate when Fano resonance hybridizes flexural and longitudinal waves and balances their radiative decay rates. We demonstrate that when the Fabry-Pérot resonance of the longitudinal wave is realized simultaneously, the TMPC formed by the elastic BIC approaches infinite quality factor. Furthermore, we show that quasi-BIC can be tuned continuously to BIC through the critical frequency of mode conversion, which offers the possibility of TMPC with an arbitrarily high quality factor. Our reported concept and physical mechanism open new routes to achieve perfect mode conversion with tunable high quality factor in elastic systems.

physics.app-ph↗

arXiv2019

On Riemann Integration in Metrizable Vector Spaces

In classical analysis, Lebesgue first proved that $\mathbb{R}$ has the property that each Riemann integrable function from $[a,b]$ into $\mathbb{R}$ is continuous almost everywhere. This property is named as the Lebesgue property. Though the Lebesgue property may be breakdown in many infinite dimensional spaces including Banach or quasi Banach spaces, to determine spaces having this property is still an interesting problem. In this paper, we study Riemann integration for vector-value functions in metrizable vector spaces and prove the fundamental theorems of calculus and primitives for continuous functions. Further we discovery that $\mathbb{R}^ω$, the countable infinite product of $\mathbb{R}$ with itself equipped with the product topology, is a metrizable vector space having the Lebesgue property and prove that $l^p(1<p\leq+\infty)$, as subspaces of $\mathbb{R}^ω$, possess the Lebesgue property although they are Banach spaces having no such property.

math.FA↗