Quantum Koopman Algorithms

arXiv:2605.19054 · quant-ph · Submitted 2026-05-18 · Read on arXiv

quant-ph

Submitted: 2026-05-18

Updated: 2026-09-17

Comments: 6+31 pages, 3 figures. Refined presentation and a simplified, improved formulation of Spectral-QKA

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Query Complexity — 8× in this paper · explained in 2 episodes
• Accuracy — 6× in this paper · explained in 1 episode
• Spectral Gap — 6× in this paper · explained in 5 episodes
• Core — 3× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Lindblad Dynamics — 3× in this paper · explained in 2 episodes
• Alignment — 2× in this paper · explained in 1 episode
• Quantum Phase Estimation (QPE) — 2× in this paper · explained in 3 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Quantum simulation of partial differential equations via Schrodingerisation: technical details
• Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions
• Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation
• Linear Combination of Hamiltonian Simulation with Commutator Scaling
• Detailed assessment of calculating drag force with quantum computers: Explicit time-evolution precludes exponential advantage for nonlinear differential equations
• An end-to-end quantum algorithm for nonlinear fluid dynamics with bounded quantum advantage
• Simulating non-trivial incompressible flows with a quantum lattice Boltzmann algorithm
• Solving the Nonlinear Vlasov Equation on a Quantum Computer
• An end-to-end quantum algorithm for weakly nonlinear plasma physics with superquadratic speedup
• Improved Convergence of Carleman-Embedded Quantum Algorithm for the Vlasov-Poisson System
• Quantum Algorithms for Nonlinear Dynamics: Revisiting Carleman Linearization with No Dissipative Conditions
• Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
• Quantum measurements and the Abelian Stabilizer Problem
• Explicit Error Bounds for Carleman Linearization
• Carleman-Fourier Linearization of Complex Dynamical Systems: Convergence and Explicit Error Bounds
• Quantum simulation of a noisy classical nonlinear dynamics
• Further improving quantum algorithms for nonlinear differential equations via higher-order methods and rescaling
• Globalizing the Carleman linear embedding method for nonlinear dynamics
• A case study against QSVT: assessment of quantum phase estimation improved by signal processing techniques
• Data-driven quantum Koopman method for simulating nonlinear dynamics

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity