arXiv subjects

S. Karthikeyan

Publications and source records attributed to S. Karthikeyan.

11 recordsLinked to original sources

arXiv2026

Blind Transpiler: An open-source library for universally blind and homomorphic quantum computations

Blind quantum computation is a cryptographic primitive that allows a limited-capability client to delegate its complex computation to a remote server without revealing its data and/or computation. This branch of quantum cryptography has been bifurcated into two distinct primitives, quantum homomorphic encryption (concerning the security of only data) and universal blind quantum computation (concerning the security of data and the computing algorithm). These primitives have immense applicability in problems like secure cloud computing, secure quantum variational algorithms, quantum federated learning, and secure multiparty computation. However, no software tools exist for the rapid prototyping of such protocols, hindering the academic interrogation for potential applications. In this paper, we describe the development of the first such library for transpiling circuits written in Qiskit to its blind counterpart, which can then be delegated in a client-server architecture without revealing the client's data and/or computation. The proposed library is designed in modular and reusable component layers, enabling easier scalability to newer BQC primitives and robustness against changes in underlying primitives. We show the implementation of these primitives to a blind variational quantum classifier for the IRIS dataset.

quant-ph↗

arXiv2025

Universal Blind Quantum Computation with Recursive Rotation Gates

Blind Quantum Computation lets a limited-capability client delegate its complex computation to a remote server without revealing its data or computation. Several such protocols have been proposed under varied quantum computing models. However, these protocols either rely on highly entangled resource states (in measurement-based models) or are based on non-parametric resource sets (in circuit-based models). These restrictions hinder the practical applicability of such an algorithm in the NISQ era, especially concerning the hybrid quantum-classical infrastructure, which depends on parametric gates. We present a protocol for universal blind quantum computation based on recursive decryption of parametric rotation gates, which does not require a highly entangled state at the server side and substantially reduces the communication rounds required for practical prototyping of secure variational algorithms.

quant-ph↗

arXiv2025

Quantum computing on encrypted data with arbitrary rotation gates

An efficient technique of computing on encrypted data allows a client with limited capability to perform complex operations on a remote fault-tolerant server without leaking anything about the input or output. Quantum computing provides information-theoretic security to solve such a problem, and many such techniques have been proposed under the premises of half-blind quantum computation. However, they are dependent on a fixed non-parametric resource set that comprises some universal combination of $H,S,T,CX, CZ$ or $CCX$ gates. In this study, we show that recursive decryption of the parametric gate, $R_z(θ)$, is possible exactly when $θ=\pmπ/2^m$ for $m\in \mathbb{Z^{+}}$, and approximately with arbitrary precision $ε$ for given $θ$. We also show that a blind algorithm based on such a technique needs at most $O(\log_2^2(π/ε))$ computation steps and communication rounds, while the techniques based on a non-parametric resource set require $O(\ln^{3.97}(1/ε))$ rounds. We use these results to propose a universal scheme of half-blind quantum computation for computing on encrypted data using arbitrary rotation gates. This substantial reduction in the depth of blind circuit is an affirmative step towards the practical application of such techniques in secure NISQ-era computing.

quant-ph↗

arXiv2024

Blow-up estimates for a system of semilinear SPDEs driven by mixed fractional Brownian motions

In this paper, we obtain the existence and finite-time blow-up for the solution to a system of semilinear stochastic partial differential equations driven by a combination of Brownian and fractional Brownian motions. Under suitable assumptions, lower and upper bounds for the finite-time blow-up solution are obtained. We provide sufficient conditions for the existence of a global weak solution to the system. Further, a lower bound for the probability of the finite-time blow-up solution of the considered system is provided by using Malliavin calculus.

math.PR↗

arXiv2024

Existence of global and explosive mild solutions of fractional reaction-diffusion system of semilinear SPDEs with fractional noise

In this paper, we investigate the existence and finite-time blow-up for the solution of a reaction-diffusion system of semilinear stochastic partial differential equations (SPDEs) subjected to a two-dimensional fractional Brownian motion given by \begin{eqnarray*} du_{1}(t,x)&=&\left[ Δ_αu_{1}(t,x)+γ_{1}u_{1}(t,x)+u^{1+β_{1}}_{2}(t,x) \right]dt &\qquad \ \ +k_{11}u_{1}(t,x)dB^{H}_{1}(t)+k_{12}u_{1}(t,x)dB^{H}_{2}(t), du_{2}(t,x)&=&\left[ Δ_αu_{2}(t,x)+γ_{2}u_{2}(t,x)+u^{1+β_{2}}_{1}(t,x) \right]dt &\qquad \ \ +k_{21}u_{2}(t,x)dB^{H}_{1}(t)+k_{22}u_{2}(t,x)dB^{H}_{2}(t), \end{eqnarray*} for $x \in \mathbb{R}^{d},\ t \geq 0$, along with \begin{equation*} \begin{array}{ll} u_{i}(0,x)=f_{i}(x), &x \in \mathbb{R}^{d}, \nonumber \end{array} \end{equation*} where $Δ_α$ is the fractional power $-(-Δ)^{\fracα{2}}$ of the Laplacian, $0<α\leq 2$ and $β_{i}>0,\ γ_{i}>0$ and $k_{ij}\geq 0, i,j=1,2$ are constants. We provide sufficient conditions for the existence of a global weak solution. Under the assumption that $β_{1}\geq β_{2}>0$ with Hurst index $ 1/2 \leq H < 1,$ we obtain the blow-up times for an associated system of random partial differential equations in terms of an integral representation of exponential functions of Brownian motions. Moreover, we provide lower and upper bounds for the finite-time blow-up of the above system of SPDEs and obtain the upper bounds for the probability of non-explosive solutions to our considered system.

math.AP↗

arXiv2024

Blow-up of stochastic semilinear parabolic equations driven by Lévy noise

The blow-up phenomena of stochastic semilinear parabolic equations with additive as well as linear multiplicative Lévy noises are investigated in this work. By suitably modifying the concavity method in the stochastic context, we establish the blow-up phenomena of such systems defined on bounded domains.

math.PR↗

arXiv2024

Lower and upper bounds for the explosion times of a system of semilinear SPDEs

In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations. Under suitable assumptions, lower and upper bounds of explosion times are obtained by using explicit solutions of an associated system of random partial differential equations and a formula due to Yor. We also provide an estimate for the probability of the finite-time blow-up. With a suitable choice of parameters, the impact of the noise on the solution is investigated. The above-obtained results are also extended for semilinear SPDEs forced by two dimensional Brownian motions.

math.AP↗

arXiv2023

Global existence and non-existence of weak solutions for non-local stochastic semilinear reaction-diffusion equations driven by a fractional noise

In the present paper, we study the existence and blow-up behavior to the following stochastic non-local reaction-diffusion equation: \begin{equation*} \left\{ \begin{aligned} du(t,x)&=\left[(Δ+γ) u(t,x)+\int_{D}u^{q}(t,y)dy -ku^{p}(t,x)+δu^{m}(t,x)\int_{D}u^{n}(t,y)dy \right]dt &\quad+ηu(t,x)dB^{H}(t), u(t,x)&=0, \ \ t>0, \ \ x\in \partial D, u(0,x)&=f(x) \geq 0, \ \ x\in D, \end{aligned} \right. \end{equation*} where $D\subset \mathbb{R}^{d}\ (d \geq 1)$ is a bounded domain with smooth boundary $\partial D$. Here, $k>0, γ, δ, η\geq 0$ and $p,q,n>1,\ m\geq 0$ with $m+n \geq q\geq p$. The initial data $f $ is a non-negative bounded measurable function in class $C^{2}$ which is not identically zero. Here, $\left\{ B^{H}(t) \right\}_{t \geq 0} $ is a one-dimensional fractional Brownian motion with Hurst parameter $\frac{1}{2} \leq H<1$ defined on a filtered probability space $\left( Ω, \mathcal{F}, (\mathcal{F}_{t})_{t \geq 0}, \mathbb{P} \right)$. First, we estimate a lower bound for the finite-time blow-up and by choosing a suitable initial data, we obtain the upper bound for the finite-time blow-up of the above equation. Next, we provide a sufficient condition for the global existence of a weak solution of the above equation. Further, we obtain the bounds for the probability of blow-up solution.

math.PR↗

arXiv2016

Weakly Supervised Localization using Deep Feature Maps

Object localization is an important computer vision problem with a variety of applications. The lack of large scale object-level annotations and the relative abundance of image-level labels makes a compelling case for weak supervision in the object localization task. Deep Convolutional Neural Networks are a class of state-of-the-art methods for the related problem of object recognition. In this paper, we describe a novel object localization algorithm which uses classification networks trained on only image labels. This weakly supervised method leverages local spatial and semantic patterns captured in the convolutional layers of classification networks. We propose an efficient beam search based approach to detect and localize multiple objects in images. The proposed method significantly outperforms the state-of-the-art in standard object localization data-sets with a 8 point increase in mAP scores.

cs.CV↗

arXiv2016

Search Tracker: Human-derived object tracking in-the-wild through large-scale search and retrieval

Humans use context and scene knowledge to easily localize moving objects in conditions of complex illumination changes, scene clutter and occlusions. In this paper, we present a method to leverage human knowledge in the form of annotated video libraries in a novel search and retrieval based setting to track objects in unseen video sequences. For every video sequence, a document that represents motion information is generated. Documents of the unseen video are queried against the library at multiple scales to find videos with similar motion characteristics. This provides us with coarse localization of objects in the unseen video. We further adapt these retrieved object locations to the new video using an efficient warping scheme. The proposed method is validated on in-the-wild video surveillance datasets where we outperform state-of-the-art appearance-based trackers. We also introduce a new challenging dataset with complex object appearance changes.

cs.CV↗

arXiv2010

A Security Based Data Mining Approach in Data Grid

Grid computing is the next logical step to distributed computing. Main objective of grid computing is an innovative approach to share resources such as CPU usage; memory sharing and software sharing. Data Grids provide transparent access to semantically related data resources in a heterogeneous system. The system incorporates both data mining and grid computing techniques where Grid application reduces the time for sending results to several clients at the same time and Data mining application on computational grids gives fast and sophisticated results to users. In this work, grid based data mining technique is used to do automatic allocation based on probabilistic mining frequent sequence algorithm. It finds frequent sequences for many users at a time with accurate result. It also includes the trust management architecture for trust enhanced security.

cs.DC↗