# Conformalized Quantum DeepONet Ensembles

Quantum DeepONet ensembles cut the hidden-layer cost of operator learning from the quadratic cost of dense layers to near-linear, and add a finite-sample, distribution-free lower bound on query-averaged coverage. Previously quantum operator learning returned only noisy point predictions, while Bayesian networks and Monte Carlo dropout offered no distribution-free guarantee. The approach replaces dense hidden layers with quantum orthogonal neural networks and applies split conformal calibration to the mean and standard deviation of independently trained ensembles. On synthetic antiderivative and advection benchmarks, relative L2 errors are 0.46% and 2.28%, with 8-model ensemble coverage of 92.13% and 88.99% against a 90% target.

Quantum DeepONet ensembles cut the hidden-layer cost of operator learning from the quadratic cost of dense layers to near-linear, and add a finite-sample, distribution-free lower bound on query-averaged coverage. Previously quantum operator learning returned only noisy point predictions, while Bayesian networks and Monte Carlo dropout offered no distribution-free guarantee. The approach replaces dense hidden layers with quantum orthogonal neural networks and applies split conformal calibration to the mean and standard deviation of independently trained ensembles. On synthetic antiderivative and advection benchmarks, relative L2 errors are 0.46% and 2.28%, with 8-model ensemble coverage of 92.13% and 88.99% against a 90% target.