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Related papers: Quantum linear systems algorithms: a primer

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Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…

Quantum Physics · Physics 2023-05-16 Ashley Montanaro , Changpeng Shao

Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient…

Quantum Physics · Physics 2019-07-12 Hai-Ling Liu , Chao-Hua Yu , Yu-Sen Wu , Shi-Jie Pan , Su-Juan Qin , Fei Gao , Qiao-Yan Wen

In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…

Quantum Physics · Physics 2008-12-24 Sarah K. Leyton , Tobias J. Osborne

Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…

Quantum Physics · Physics 2025-11-04 Nhat A. Nghiem

We present a novel quantum high-dimensional linear regression algorithm with an $\ell_1$-penalty based on the classical LARS (Least Angle Regression) pathwise algorithm. Similarly to available classical algorithms for Lasso, our quantum…

Quantum Physics · Physics 2025-03-26 Joao F. Doriguello , Debbie Lim , Chi Seng Pun , Patrick Rebentrost , Tushar Vaidya

This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in…

Quantum Physics · Physics 2022-08-09 Armando Bellante , Alessandro Luongo , Stefano Zanero

Practical applicability of quantum optimisation on near term devices is constrained by limited qubit counts and hardware noise, which restricts the scalability of quantum optimisation algorithms for combinatorial problems. The simulation of…

Quantum Physics · Physics 2026-05-01 Namasi G Sankar , Georgios Miliotis , Simon Caton

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…

Quantum Physics · Physics 2021-11-10 Andrew M. Childs , Jin-Peng Liu , Aaron Ostrander

Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…

As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…

Quantum Physics · Physics 2025-07-24 Di Fang , David Lloyd George , Yu Tong

This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…

Quantum Physics · Physics 2025-12-02 Jorge J. Martínez de Lejarza

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…

Quantum Physics · Physics 2024-09-10 Weitao Lin , Guojing Tian , Xiaoming Sun

Quantum computing is evolving so rapidly that it forces us to revisit, rewrite, and update the foundations of the theory. \emph{Basic Quantum Algorithms} revisits the earliest quantum algorithms. The journey began in 1985 with Deutsch…

Quantum Physics · Physics 2026-04-09 Renato Portugal

We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…

Quantum Physics · Physics 2025-04-02 Nhat A. Nghiem

The Hidden Quantum Markov Model (HQMM) has significant potential for analyzing time-series data and studying stochastic processes in the quantum domain as an upgrading option with potential advantages over classical Markov models. In this…

Quantum Physics · Physics 2024-11-01 Xiao-Yu Li , Qin-Sheng Zhu , Yong Hu , Hao Wu , Guo-Wu Yang , Lian-Hui Yu , Geng Chen

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…

Quantum Physics · Physics 2023-02-14 Mohammadhossein Mohammadisiahroudi , Ramin Fakhimi , Tamás Terlaky

Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…

Quantum Physics · Physics 2024-09-11 Gloria Turati , Alessia Marruzzo , Maurizio Ferrari Dacrema , Paolo Cremonesi

We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…

We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…

Quantum Physics · Physics 2019-03-15 Peng Qian , Wei-Cong Huang , Gui-Lu Long

Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…