Speaker
Description
We present quantum algorithms that implement a class of exponentially large Neural Differential Equations (Neural ODEs) on quantum computers using only polynomial quantum resources. Neural ODEs define the forward propagation of a neural network as the solution of a nonlinear differential equation, so from this viewpoint, the forward pass (inference) becomes a simulation problem. We show that this simulation problem can be solved efficiently with quantum algorithms when the Neural ODE satisfies Carleman convergence conditions. Furthermore, for classification tasks, we present subroutines that prepare the softmax output state directly for sampling. To learn such a network from data, we avoid variational loops entirely and cast training as closed-form regression using QSVT-based techniques, introducing a block-encoded matrix-logarithm subroutine and a Carleman-constrained learner. Finally, we prove that Neural ODE simulation is BQP-complete, giving strong evidence for quantum advantage. Together, these results show that treating neural networks as continuous-time dynamical systems opens a route to provable quantum advantage for machine learning.
| Topic | Quantum algorithms for machine learning applications |
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