Latent-space quantum surrogate performs Bayesian inversion of heterogeneous conductivity on IonQ and Rigetti NISQ hardware

The authors reduce high-dimensional conductivity fields via principal-component analysis and encode the forward response with a convolutional autoencoder, then train a hybrid quantum-classical circuit to learn the latent mapping. Stochastic variational inference runs entirely inside this compressed space, avoiding direct embedding of full grids into near-term registers. Demonstrations cover both informative and non-informative priors on synthetic one- and two-dimensional conductivity distributions.

Hardware tests on the IonQ simulator and Rigetti Cepheus-1-108Q processor show that a lightweight learned denoiser restores accuracy to within a few percent of noiseless classical results. This hybrid workflow therefore sidesteps the dimensionality barrier that has blocked earlier quantum surrogate attempts while still exploiting NISQ-era circuit expressivity.

The approach directly addresses ill-posed inverse problems in non-destructive testing and medical imaging where repeated high-fidelity forward solves dominate cost. By keeping all Bayesian updates in latent space it also opens a route to uncertainty quantification that scales with qubit count rather than grid size.

A key untested step remains end-to-end execution on larger, less noisy devices; the current residual error after denoising indicates that further circuit-depth or error-mitigation gains will be required before the method displaces mature classical reduced-order models in production settings.