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We propose a novel QTGNN framework for detecting fraudulent transactions in large-scale financial networks. By integrating quantum embedding, variational graph convolutions, and topological data analysis, QTGNN captures complex transaction…
Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast…
Quantum computing requires effective error correction strategies to mitigate noise and decoherence. Quantum Low-Density Parity-Check (QLDPC) codes have emerged as a promising solution for scalable Quantum Error Correction (QEC) applications…
We study quantum advantage in one-step rendezvous games on simple graphs analytically, numerically, and using noisy intermediate-scale quantum (NISQ) processors. Our protocols realise the recently discovered [arXiv:2207.14404] optimal…
Using a cyclotron based model problem, we demonstrate for the first time the applicability and usefulness of a uncertainty quantification (UQ) approach in order to construct surrogate models for quantities such as emittance, energy spread…
In the last few decades, uncertainty quantification (UQ) methods have been used widely to ensure the robustness of engineering designs. This chapter aims to detail recent advances in popular uncertainty quantification methods used in…
Quasi-Monte Carlo (QMC) integration over unbounded domains $\mathbb{R}^s$ remains challenging due to the high dimensionality of sampling space and the boundary growth of the integrand. In applications such as uncertainty quantification…
We show that currently available noisy intermediate-scale quantum (NISQ) computers can be used for versatile quantum simulations of chaotic systems. We introduce a novel classical-quantum hybrid approachfor exploring the dynamics of the…
There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…
Advancements in Noisy Intermediate-Scale Quantum (NISQ) computing are steadily pushing these systems toward outperforming classical supercomputers on specific, well-defined computational tasks. In this work, we explore and control quantum…
Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…
We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of…
Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix…
In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the…
The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical…
We propose a new method for evaluating NISQ devices. This paper has three distinct parts. First, we present a new quantum algorithm that solves a two hundred year old problem of finding quadratic nonresidues (QNR) in polynomial time. We…
Parametric uncertainty in nonlinear dynamical systems can fundamentally alter bifurcation behaviour, leading to qualitative response changes. Predicting operating margins/envelopes under such uncertainties is critical but challenging:…
This work introduces the network uncertainty quantification (NetUQ) method for performing uncertainty propagation in systems composed of interconnected components. The method assumes the existence of a collection of components, each of…
With the rapid growth of interconnected devices, accurately detecting malicious activities in network traffic has become increasingly challenging. Most existing deep learning-based intrusion detection systems treat network flows as…
Designing chaotic maps with complex dynamics is a challenging topic. This paper introduces the nonlinear chaotic processing (NCP) model, which contains six basic nonlinear operations. Each operation is a general framework that can use…