Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
Quantum algorithm for linear differential equations with exponentially improved dependence on precision
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
A hybrid quantum-classical variational method using polynomial approximations to the energy functional enables finite element analysis of a 1D Neo-Hookean hyperelastic model on near-term quantum hardware.
citing papers explorer
-
Trainable Quantum Spectral Models for Partial Differential Equations
Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
-
A Variational Quantum Algorithm for Nonlinear Finite Element Analysis of Hyperelastic Materials
A hybrid quantum-classical variational method using polynomial approximations to the energy functional enables finite element analysis of a 1D Neo-Hookean hyperelastic model on near-term quantum hardware.