Quantum algorithm for simulating the wave equation
TL;DR: In this paper, a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions is presented, which uses Hamiltonian simulation and quantum linear system algorithms as subroutines.
read more
Abstract: We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for polynomially improved scaling in truncation errors and improved scaling for state preparation relative to general purpose quantum algorithms for solving linear differential equations. Relative to classical algorithms for simulating the $D$-dimensional wave equation, our quantum algorithm achieves exponential space savings and achieves a speedup which is polynomial for fixed $D$ and exponential in $D$. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Quantum Computing in the NISQ era and beyond
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future as mentioned in this paper, which will be useful tools for exploring many-body quantum physics, and may have other useful applications.
Quantum Computing in the NISQ era and beyond
John Preskill
- 06 Aug 2018
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future, and the 100-qubit quantum computer will not change the world right away - but it should be regarded as a significant step toward the more powerful quantum technologies of the future.
Efficient quantum algorithm for dissipative nonlinear differential equations.
Jin-Peng Liu,Herman Oie Kolden,Herman Oie Kolden,Hari Krovi,Nuno Loureiro,Konstantina Trivisa,Andrew M. Childs +6 more
TL;DR: A lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations is provided, showing that the problem is intractable for $R \ge \sqrt{2}$.
217
Quantum Computing and Communications: An Engineering Approach
Sandor Imre,Ferenc Balázs +1 more
- 01 Jan 2005
TL;DR: This book discusses quantum computing basics, quantum Fourier Transform, and other topics related to quantum computing, as well as some examples of applications.
215
Solving nonlinear differential equations with differentiable quantum circuits
TL;DR: A hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions is described, and how this approach can implement a spectral method for solving differential equations in a high-dimensional feature space is shown.
References
A family of embedded Runge-Kutta formulae
J. R. Dormand,P.J. Prince +1 more
TL;DR: In this article, a family of embedded Runge-Kutta formulae RK5 (4) are derived from these and a small principal truncation term in the fifth order and extended regions of absolute stability.
3.7K
Quantum algorithm for linear systems of equations.
TL;DR: This work exhibits a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa, and proves that any classical algorithm for this problem generically requires exponentially more time than this quantum algorithm.
A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method
TL;DR: In this article, a discrete variable representation (DVR) is introduced for use as the L2 basis of the S-matrix version of the Kohn variational method for quantum reactive scattering.
•Book
Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems
Randall J. LeVeque
- 06 Sep 2007
TL;DR: This book discusses infinite difference approximations, Iterative methods for sparse linear systems, and zero-stability and convergence for initial value problems for ordinary differential equations.