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The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here we present two algorithms that, in conjunction with other methods developed…

Quantum Physics · Physics 2025-12-30 Debadrita Saha , Philip Richerme , Srinivasan S. Iyengar

We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} ,…

Quantum Physics · Physics 2026-04-08 Nhat A. Nghiem , Tzu-Chieh Wei

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…

Quantitative Methods · Quantitative Biology 2016-04-29 Jonathan U. Harrison , Christian A. Yates

We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…

Quantum Physics · Physics 2020-01-15 Michael Lubasch , Jaewoo Joo , Pierre Moinier , Martin Kiffner , Dieter Jaksch

This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…

Quantum Physics · Physics 2012-05-21 Igor G. Vladimirov , Ian R. Petersen

We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…

Quantum Physics · Physics 2025-04-18 Hsin-Yu Wu , Annie E. Paine , Evan Philip , Antonio A. Gentile , Oleksandr Kyriienko

We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization…

Quantum Physics · Physics 2020-12-07 Nobuyuki Yoshioka , Yuya O. Nakagawa , Kosuke Mitarai , Keisuke Fujii

We propose a quantum algorithm that simulates the propagation of a light field through a weakly inhomogeneous medium. The wave equation in the paraxial approximation in inhomogeneous material takes the form of the Schr\"odinger equation…

Quantum Physics · Physics 2026-04-01 Siavash Davani , Martin Gärttner , Falk Eilenberger

Quantum simulation holds the promise of improving the atomic simulations used at EDF to anticipate the ageing of materials of interest. One simulator in particular seems well suited to modeling interacting electrons: the Rydberg atoms…

Quantum Physics · Physics 2024-06-21 Antoine Michel

In light of recent exciting progress in building up quantum computing facilities based on both optical and cold-atom techniques, the algorithms for quantum simulations of particle-physics systems are in rapid progress. In this paper, we…

High Energy Physics - Phenomenology · Physics 2021-05-12 Ying Chen , Yunheng Ma , Shun Zhou

Classical-quantum hybrid algorithms have recently garnered significant attention, which are characterized by combining quantum and classical computing protocols to obtain readout from quantum circuits of interest. Recent progress due to…

Quantum Physics · Physics 2026-01-05 Pete Rigas

Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…

Quantum Physics · Physics 2026-03-19 Wataru Setoyama , Keisuke Fujii

Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [6] to handle this kind of problems. The…

Numerical Analysis · Mathematics 2010-09-20 Francis Filbet , Jingwei Hu , Shi Jin

We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…

Quantum Physics · Physics 2026-03-18 Ahmet Burak Catli , Sophia Simon , Nathan Wiebe

Quantum simulation has primarily focused on unitary dynamics, while many physical and engineering systems can be modeled by linear ordinary differential equations whose generators include non-Hermitian terms. Recent studies have shown that…

Quantum Physics · Physics 2025-10-06 Seonggeun Park

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…

Systems and Control · Electrical Eng. & Systems 2024-09-17 Zexin Sun , Mingyu Chen , John Baillieul

A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is…

Quantum Physics · Physics 2015-06-26 V. P. Belavkin

The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…

Numerical Analysis · Mathematics 2021-11-30 Pascal Heid , Thomas P. Wihler

We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…

Computational Physics · Physics 2019-03-27 Narain Karedla , Jan Christoph Thiele , Ingo Gregor , Jörg Enderlein

We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing…

Quantum Physics · Physics 2025-08-20 Kushagra Garg , Zeeshan Ahmed , Subhadip Mitra , Shantanav Chakraborty