On the numerical limitations of dual Koopman von Neumann embeddings for solving conservative nonlinear ordinary differential equations on quantum computers

arXiv:2609.28999 · quant-ph, math-ph, math.MP · Submitted 2026-09-24 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-09-24

Updated: 2026-09-25

Terminology

• Accuracy — 7× in this paper · explained in 1 episode
• Reconstruction Error — 6× in this paper · explained in 2 episodes
• Benchmark — 4× in this paper · explained in 2 episodes
• Block Encoding — 3× in this paper · explained in 4 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Koopman-von Neumann — 2× in this paper
• Quantization — 2× in this paper · explained in 12 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Unitary Dynamics — 2× in this paper · explained in 2 episodes
• Approximate Counting — 1× in this paper · explained in 1 episode
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Quantum Fourier Transform — 1× in this paper

Sources

• A quantum algorithm to solve nonlinear differential equations
• Quantum algorithm for the advection-diffusion equation and the Koopman-von Neumann approach to nonlinear dynamical systems
• A Polynomial Time Quantum Algorithm for Exponentially Large Scale Nonlinear Differential Equations via Hamiltonian Simulation
• Globalizing the Carleman linear embedding method for nonlinear dynamics
• Do not Waste Money on Advertising Spend: Bid Recommendation via Concavity Changes

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