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We propose an easy-to-implement iterative method for resolving the implicit (or semi-implicit) schemes arising in solving reaction-diffusion (RD) type equations. We formulate the nonlinear time implicit scheme as a min-max saddle point…

Numerical Analysis · Mathematics 2023-05-09 Shu Liu , Siting Liu , Stanley Osher , Wuchen Li

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

In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…

Numerical Analysis · Computer Science 2013-04-23 P. N. Vabishchevich , V. I. Vasil'ev

In this work, we propose the Residual-Weighted Physics-Informed Neural Network (RW-PINN), a new method designed to enhance the accuracy of Physics-Informed Neural Network (PINN) based algorithms. We construct a deep learning framework with…

Numerical Analysis · Mathematics 2025-09-03 K. Murari , P. Roul , S. Sundar

We propose an approach to measure the quantum phase of an electron in a non-Abelian system using the algorithm of Quantum Phase Estimation (QPE). The discrete-path systems were previously studied in the context of square or rectangular…

Quantum Physics · Physics 2025-09-15 Seng Ghee Tan , Son-Hsien Chen , Ying-Cheng Yang , Yen-Fu Chen , Yen-Lin Chen , Chia-Hsiu Hsieh

The search for new computational tasks of quantum chemistry that can be performed on current quantum computers is important for the development of quantum computing and quantum chemistry. Although calculations of chemical reactions have a…

Quantum Physics · Physics 2022-04-01 Shu Kanno

Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…

Quantum Physics · Physics 2021-08-27 Kazuya Kaneko , Koichi Miyamoto , Naoyuki Takeda , Kazuyoshi Yoshino

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…

Quantum Physics · Physics 2025-12-16 Dong An , Andrew M. Childs , Lin Lin

We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…

Numerical Analysis · Mathematics 2013-03-25 Mårten Gulliksson , Sverker Edvardsson , Andreas Lind

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems…

Computational Physics · Physics 2023-06-16 Katherine Asztalos , René Steijl , Romit Maulik

Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed…

Numerical Analysis · Mathematics 2020-10-07 Seyeon Lee , Junseo Lee , Hyunju Kim , Bongsoo Jang

Quantum computing is a promising technology that accelerates the partial differential equations solver for practical problems. The reconstruction of solutions (i.e., the readout of quantum states) remains a crucial problem, although…

Quantum Physics · Physics 2025-11-26 Xinchi Huang , Hirofumi Nishi , Yoshifumi Kawada , Tomofumi Zushi , Yu-ichiro Matsushita

Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale $L$ increases with time. The so-called coarsening exponent $n$ characterizes the time dependence of the…

Pattern Formation and Solitons · Physics 2013-06-11 Matteo Nicoli , Chaouqi Misbah , Paolo Politi

This study examines the potential for fault-tolerant quantum computers to provide utility in fluid dynamics simulations, with a focus on drag force calculations for ship hull design. We assess whether quantum algorithms can surpass…

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…

Plasma Physics · Physics 2023-06-21 Abtin Ameri , Paola Cappellaro , Hari Krovi , Nuno F. Loureiro , Erika Ye

A novel quantum algorithm for solving the Boltzmann-Maxwell equations of the 6D collisionless plasma is proposed. The equation describes the kinetic behavior of plasma particles in electromagnetic fields and is known for the classical…

Plasma Physics · Physics 2023-06-12 Hayato Higuchi , Juan William Pedersen , Akimasa Yoshikawa

Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging…

Quantum Physics · Physics 2026-05-19 Arthur G. Rattew , Po-Wei Huang , Naixu Guo , Lirandë Pira , Patrick Rebentrost

In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…

Quantum Physics · Physics 2018-10-04 M. Chiew , K. de Lacy , C. H. Yu , S. Marsh , J. B. Wang

Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…

Quantum Physics · Physics 2021-12-28 Debajyoti Bera , Tharrmashastha Sapv

We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…

Quantum Physics · Physics 2018-10-16 Apoorva Patel , Anjani Priyadarsini