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Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable…

Fluid Dynamics · Physics 2025-05-20 Zhixin Song , Robert Deaton , Bryan Gard , Spencer H. Bryngelson

Quantum computing has made tremendous progress in recent years, providing potentialities for breaking the bottleneck of computing power in the field of scientific computing, like computational fluid dynamics. To reduce computational costs…

Quantum Physics · Physics 2025-05-05 Li Xu , Ming Li , Lei Zhang , Hai Sun , Jun Yao

We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…

Quantum Physics · Physics 2021-05-20 Oleksandr Kyriienko , Annie E. Paine , Vincent E. Elfving

In this paper, we describe and experimentally demonstrate an error detection scheme that does not employ ancilla qubits or mid-circuit measurements. This is achieved by expanding the Hilbert space where a single logical qubit is encoded…

Quantum Physics · Physics 2022-04-26 Nicolas J. Guerrero , David E. Weeks

In this paper we present a general framework for solving the stationary nonlinear Schr\"odinger equation (NLSE) on a network of one-dimensional wires modelled by a metric graph with suitable matching conditions at the vertices. A formal…

Pattern Formation and Solitons · Physics 2016-05-05 Sven Gnutzmann , Daniel Waltner

We present quantum algorithms for simulating the dynamics of a broad class of classical oscillator systems containing $2^n$ coupled oscillators (Eg: $2^n$ masses coupled by springs), including those with time-dependent forces, time-varying…

Quantum Physics · Physics 2025-05-26 Abhinav Muraleedharan , Nathan Wiebe

We develop three new methods to implement any Linear Combination of Unitaries (LCU), a powerful quantum algorithmic tool with diverse applications. While the standard LCU procedure requires several ancilla qubits and sophisticated…

Quantum Physics · Physics 2024-10-16 Shantanav Chakraborty

We demonstrate that certain vortices in spinor Bose-Einstein condensates are non-Abelian anyons and may be useful for topological quantum computation. We perform numerical experiments of controllable braiding and fusion of such vortices,…

Quantum Gases · Physics 2019-10-09 Thomas Mawson , Timothy Petersen , Joost Slingerland , Tapio Simula

Evolution by the Gross-Pitaevskii equation, which describes Bose-Einstein condensates under certain conditions, solves the unstructured search problem more efficiently than does the Schr\"odinger equation, because it includes a cubic…

Quantum Physics · Physics 2014-01-21 David A. Meyer , Thomas G. Wong

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a…

Quantum Physics · Physics 2016-02-24 Hayato Goto

We propose a framework to solve non-linear and history-dependent mechanical problems based on a hybrid classical computer -- quantum annealer approach. Quantum Computers are anticipated to solve particular operations exponentially faster.…

Computational Engineering, Finance, and Science · Computer Science 2024-02-20 Van-Dung Nguyen , Ling Wu , Françoise Remacle , Ludovic Noels

We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…

Optics · Physics 2026-04-01 Jérémy Itier , Gilles Renversez , Frédéric Zolla

Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by…

Pattern Formation and Solitons · Physics 2021-08-04 A. S. Carstea , A. Ludu

Many quantum algorithms make use of ancilla, additional qubits used to store temporary information during computation, to reduce the total execution time. Quantum computers will be resource-constrained for years to come so reducing ancilla…

Quantum Physics · Physics 2020-02-26 Jonathan M. Baker , Casey Duckering , Frederic T. Chong

We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…

Quantum Physics · Physics 2014-03-20 Chris D. Richardson , Peter Schlagheck , John Martin , Nicolas Vandewalle , Thierry Bastin

We have realized the nonlinear sign shift (NS) operation for photonic qubits.This operation shifts the phase of two photons reflected by a beam splitter using an extra single photon and measurement. We show that the conditional phase shift…

Quantum Physics · Physics 2009-11-10 Kaoru Sanaka , Thomas Jennewein , Jian-Wei Pan , Kevin Resch , Anton Zeilinger

Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and…

To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is…

Quantum Physics · Physics 2026-04-02 Peng Guo , Paul LeVan , Frank X. Lee , Yong Zhao

An exact analytical solution is derived for the wavefunction of an electron in a one-dimensional moving quantum dot in a nanowire, in the presence of time-dependent spin-orbit coupling. For cyclic evolutions we show that the spin of the…

Quantum Physics · Physics 2015-06-18 T. Cadez , J. H. Jefferson , A. Ramsak

Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…

Quantum Physics · Physics 2026-01-29 Alisa D. Manukhova , Andrey A. Rakhubovsky , Radim Filip