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The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy intermediate-scale quantum (NISQ) devices. A particular application is to obtain ground…

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

Optimization and Control · Mathematics 2026-04-01 John Chiang

Before the availability of large scale fault-tolerant quantum devices, one has to find ways to make the most of current noisy intermediate-scale quantum devices. One possibility is to seek smaller repetitive hybrid quantum-classical tasks…

Quantum Physics · Physics 2023-04-12 Teiko Heinosaari , Daniel Reitzner , Alessandro Toigo

The preparation of Hamiltonian eigenstates is essential for many applications in quantum computing; the efficiency with which this can be done is of key interest. A canonical approach exploits the quantum phase estimation (QPE) algorithm.…

Quantum Physics · Physics 2022-12-05 Richard Meister , Simon C. Benjamin

The manifestation of the wave nature of light through diffraction imposes limits on the resolution of optical imaging. For over a century, the Abbe-Rayleigh criterion has been utilized to assess the spatial resolution limits of optical…

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh case, no closed-form expressions for…

Information Theory · Computer Science 2011-04-13 Florian Dupuy , Philippe Loubaton

Quantum illumination (QI) promises unprecedented performances in target detection but there are various problems surrounding its implementation. Where target ranging is a concern, signal and idler recombination forms a crucial barrier to…

Quantum Physics · Physics 2020-11-10 Athena Karsa , Stefano Pirandola

This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…

Numerical Analysis · Mathematics 2022-02-17 Yuji Nakatsukasa , Joel A. Tropp

The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper…

Numerical Analysis · Mathematics 2026-05-05 Biswarup Karmakar , Neha Bhadala , Ratikanta Behera

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…

Optimization and Control · Mathematics 2025-05-06 Youran Dong , Junfeng Yang , Wei Yao , Jin Zhang

We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix $M\in\mathbb{C}^{n\times n}$ up to backward error $\delta\|M\|$ in…

Numerical Analysis · Mathematics 2022-05-16 Jess Banks , Jorge Garza-Vargas , Nikhil Srivastava

We study the computation of the $\alpha$-R\'enyi capacity of a classical-quantum (c-q) channel for $\alpha\in(0,1)$. We propose an exponentiated-gradient (mirror descent) iteration that generalizes the Blahut-Arimoto algorithm. Our analysis…

Quantum Physics · Physics 2026-01-16 Yu-Hong Lai , Hao-Chung Cheng

Quantum illumination (QI) is an entanglement-based protocol for improving lidar/radar detection of unresolved targets beyond what a classical lidar/radar of the same average transmitted energy can do. Originally proposed by Lloyd as a…

Quantum Physics · Physics 2024-09-20 Jeffrey H. Shapiro

We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by…

Quantum Physics · Physics 2021-07-26 Kenneth Choi , Dean Lee , Joey Bonitati , Zhengrong Qian , Jacob Watkins

We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…

Optimization and Control · Mathematics 2022-12-14 Dewei Zhang , Sam Davanloo Tajbakhsh

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

Quantum Physics · Physics 2023-05-02 Shantanav Chakraborty , Aditya Morolia , Anurudh Peduri

Decoded Quantum Interferometry (DQI) is a recently introduced quantum algorithm that reduces discrete optimization to decoding with potential advantages over the best-known polynomial-time classical algorithms for certain Max-LINSAT…

Quantum Physics · Physics 2026-05-19 Kaifeng Bu , Weichen Gu , Xiang Li

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…

Numerical Analysis · Mathematics 2016-11-23 Ruihao Huang , Allan A. Struthers , Jiguang Sun , Ruming Zhang

Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…

Quantum Physics · Physics 2024-09-25 S. M. Lim , C. E. Susa , R. Cohen

The Variational Quantum Eigensolver (VQE) is widely regarded as a promising algorithm for calculating ground states of quantum systems that are intractable for classical computers. This promise is typically motivated by the hope of…

Quantum Physics · Physics 2026-04-13 Manuel Hagelueken , David A. Kreplin , Florian Wieland , Marco F. Huber , Marco Roth