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We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not…

Quantum Physics · Physics 2024-07-25 Alet Roux , Tomasz Zastawniak

The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to…

Machine Learning · Computer Science 2021-07-01 Armin Moharrer , Khashayar Kamran , Edmund Yeh , Stratis Ioannidis

Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…

Quantum Physics · Physics 2014-02-19 Jian Pan , Yudong Cao , Xiwei Yao , Zhaokai Li , Chenyong Ju , Xinhua Peng , Sabre Kais , Jiangfeng Du

The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…

Quantum Physics · Physics 2025-09-22 Yuxuan Du , Min-Hsiu Hsieh , Dacheng Tao

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Machine Learning · Computer Science 2024-10-28 Shudian Zhao , Jan Kronqvist

Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…

Quantum Physics · Physics 2021-04-07 Keren Li , Pan Gao , Shijie Wei , Jiancun Gao , Guilu Long

We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. Several classical textbook algorithms have quite efficient expected-runtime complexity, whereas…

Programming Languages · Computer Science 2017-05-02 Krishnendu Chatterjee , Hongfei Fu , Aniket Murhekar

The emerging field of learning-augmented online algorithms uses ML techniques to predict future input parameters and thereby improve the performance of online algorithms. Since these parameters are, in general, real-valued functions, a…

Machine Learning · Computer Science 2022-05-26 Keerti Anand , Rong Ge , Amit Kumar , Debmalya Panigrahi

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

Statistics Theory · Mathematics 2021-05-18 Arun Kumar Kuchibhotla , Lawrence D. Brown , Andreas Buja , Edward I. George , Linda Zhao

Large-scale sequential data is often exposed to some degree of inhomogeneity in the form of sudden changes in the parameters of the data-generating process. We consider the problem of detecting such structural changes in a high-dimensional…

Methodology · Statistics 2016-01-15 Florencia Leonardi , Peter Bühlmann

We present regression and compression algorithms for lattice QCD data utilizing the efficient binary optimization ability of quantum annealers. In the regression algorithm, we encode the correlation between the input and output variables…

High Energy Physics - Lattice · Physics 2021-12-07 Boram Yoon , Chia Cheng Chang , Garrett T. Kenyon , Nga T. T. Nguyen , Ermal Rrapaj

Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…

Quantum Physics · Physics 2023-12-07 David Peral García , Juan Cruz-Benito , Francisco José García-Peñalvo

This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…

Data Structures and Algorithms · Computer Science 2021-12-01 Erik D. Demaine , Jayson Lynch , Jiaying Sun

Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization…

The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…

Statistics Theory · Mathematics 2023-06-30 Claire Boyer , Antoine Godichon-Baggioni

Linear Discriminant Analysis (LDA) is a fundamental method for classification. Its simple linear structure facilitates interpretation, and it is naturally suited to multi-class settings. LDA is also closely connected to several classical…

Methodology · Statistics 2026-04-09 Xin Bing , Bingqing Li , Marten Wegkamp

We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…

Numerical Analysis · Mathematics 2019-03-27 Yuhan Ding , Fred J. Hickernell , Peter Kritzer , Simon Mak

Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…

Quantum Physics · Physics 2024-06-19 Dominic W. Berry , Pedro C. S. Costa

We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…

Computational Complexity · Computer Science 2019-07-24 Debajyoti Bera , Tharrmashastha P.

In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is…

Quantum Physics · Physics 2021-03-08 Julien Gacon , Christa Zoufal , Stefan Woerner