To test the potential of so-called quantum physics-informed neural network technology for solving evolutionary partial differential equations, the problem of multiple wave propagation in a weakly nonlinear medium described by the Korteweg-de Vries equation with periodic boundary conditions is considered.
Abstract
To test the potential of so-called quantum physics-informed neural network (QPINN) technology for solving evolutionary partial differential equations, we consider the problem of multiple wave propagation in a weakly nonlinear medium described by the Korteweg-de Vries equation with periodic boundary conditions. Although this problem is solvable analytically, high-genus solutions could represent a rather challenging testbed for numerical methods. Therefore, our idea is to test whether a QPINN is sufficiently mature for application in this context by providing a set of indicators of merit and performing several numerical experiments.
This work proves that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE.
We present a computational module for upper-level undergraduate quantum mechanics and computational physics courses in which neural networks serve as variational trial wave functions for the Rayleigh–Ritz method. Spatial derivatives are evaluated using automatic differentiation. The infinite square well and harmonic os...
Xiao-Bo Guo, Hao-Ran Gu· European journal of physics· 0 citations
Introduction. Physics-informed neural networks (PINNs) are increasingly proposed as universal solvers of differential equations, but their reliability for nonlinear oscillators with several periodic solutions is insufficiently studied. Aims and objectives. To compare D.S. Dzhumabaev’s parametrization method with PINNs...
A. E. Kim· НАУКА ИНТЕЛЛЕКТУАЛЬНЫХ СИСТЕ...· 0 citations
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a transformative change for many industries. In a recent breakthrough [Liu et al....
David Jennings, K. Korzekwa, Matteo Lostaglio et al.· Quantum· 21 citations· ⚡5
Physics-Informed Neural Networks (PINNs) are a machine-learning framework for approximating solutions to systems of partial differential equations by constraining neural networks to satisfy the underlying physical laws. The resulting continuous representation does not require a predefined computational mesh and can be...
J. A. Carretero, Jorge F. Urbán, F. Abalos et al.· 2 citations
This work uses the Weyl variable and the exact Hermite moments and quantum singular value transformation to treat the polynomial and Fourier components of the potential, resulting in a quantum algorithm efficient for all ranges of wavelengths.
Shi Jin, Chu-Wen Ma· 0 citations
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