05 · Phase space
Quantum kernels for chaos
Structured Quantum Kernels for Chaotic Forecasting · arXiv 2609.13360
AeRot: amplitude encoding of normalised delay windows plus one layer of single-qubit rotations that assigns contiguous blocks of time steps to each qubit. Kernel ridge regression on Lorenz-63, bandwidths cross-validated over 100 seeds, beats tuned RBF and Matérn-5/2 kernels at horizons of 0.15 time units and beyond. The gain is a finite-sample inductive-bias effect, localised to the unstable saddle-approach windows — not a computational speedup.
Chaos has a shape: two moments that look identical can be headed to opposite halves of it. A small quantum circuit, used as a similarity measure, keeps track of which way a trajectory is about to turn where ordinary methods blur the two together.
- 83%of the hardest windows won
- 5–8qubits
- 100seeds