A Quantum Path to Partial Differential Equations

This open book gives an introductory path into quantum algorithms for partial differential equations. The emphasis is on block encoding, quantum singular value transformation, Hamiltonian simulation, finite difference and finite element discretizations, and the end-to-end cost of preparing and measuring PDE quantities of interest.

Suggested citation

@article{Li2026QuantumPathPDE,
  author    = {Li, Xiantao},
  title     = {A Quantum Path to Partial Differential Equations},
  year      = {2026},
  journal={arXiv preprint 	arXiv:2607.09639},  
  edition   = {Version 1.0},
  url       = {https://quantumpde.org}
}

Table of contents

1. Basic elements of quantum algorithms
2. Elliptic partial differential equations
3. Hyperbolic partial differential equations and wave equations
4. Parabolic partial differential equations and heat equations
5. A first look at nonlinear problems

Preview

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Errata and feedback

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