Quantum Koopman Algorithms — Draconitic Research

Abstract

Solving high-dimensional dynamical systems by encoding their state in the amplitudes of a quantum state is expected to be a core application of fault-tolerant quantum computers. However, the conditions under which this paradigm yields quantum advantage can be restrictive, motivating complementary approaches. Here, we introduce Quantum Koopman Algorithms, where quantum amplitudes encode approximately closed sets of observables for a linear or nonlinear dynamics. These amplitudes evolve under the Koopman operator, and we establish conditions for efficient quantum algorithms addressing both dynamical and spectral problems. With this approach, we show that classes of open-system dynamics involving exponentially large fermionic systems can be efficiently simulated on a quantum computer. For nonlinear dynamics, we introduce a novel nonlinear interaction picture that enables quantum simulation beyond existing weak-nonlinearity conditions, and extract late-time spectral data where quantum phase estimation is unavailable.

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BibTeX RIS

BibTeX

@misc{jennings2026quantum,
  title = {{Quantum Koopman Algorithms}},
  author = {David Jennings and Kamil Korzekwa and Matteo Lostaglio and Guoming Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.19054},
  eprint = {2605.19054},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.19054},
}

RIS

TY  - UNPB
TI  - Quantum Koopman Algorithms
AU  - David Jennings
AU  - Kamil Korzekwa
AU  - Matteo Lostaglio
AU  - Guoming Wang
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2605.19054
UR  - https://arxiv.org/abs/2605.19054
AB  - Solving high-dimensional dynamical systems by encoding their state in the amplitudes of a quantum state is expected to be a core application of fault-tolerant quantum computers. However, the conditions under which this paradigm yields quantum advantage can be restrictive, motivating complementary approaches. Here, we introduce Quantum Koopman Algorithms, where quantum amplitudes encode approximately closed sets of observables for a linear or nonlinear dynamics. These amplitudes evolve under the Koopman operator, and we establish conditions for efficient quantum algorithms addressing both dynamical and spectral problems. With this approach, we show that classes of open-system dynamics involving exponentially large fermionic systems can be efficiently simulated on a quantum computer. For nonlinear dynamics, we introduce a novel nonlinear interaction picture that enables quantum simulation beyond existing weak-nonlinearity conditions, and extract late-time spectral data where quantum phase estimation is unavailable.
ER  -

Abstract

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