Speaker
Description
We propose an approach for constructing multivariate probability distributions with efficient pre-training, compatible with the train-on-classical deploy-on-quantum workflow. We build models in a latent space, selecting modes that are defined by orthogonal transformations (Fourier, Hadamard, IQP etc). Starting from a uniform state of equal mode amplitudes, imaginary-time filtering reweights these amplitudes such that the resulting state matches a low-degree approximation of the empirical target distribution. This filtering can be recast as a linear combination of unitaries (LCU) circuit and corresponds to a post-selected instantaneous quantum polynomial-time (IQP) circuit. The developed approach provides a data-informed pre-training step without variational optimisation, which can subsequently be refined by an additional IQP layer to yield a forrelation-type probabilistic model.
Once the latent-space representation is learnt, a fixed-basis transformation maps it to the computational basis, enabling fast sampling and a separation between classical training and quantum deployment. The resulting models belong to a hard-to-sample family while remaining trainable with classical estimators. Crucially, coherent filtering can also be realised by unitary state preparation, up to an irrelevant normalisation factor, making pre-training deterministic.
We apply the approach to a four-dimensional probability distribution with complex marginal structure and rich correlations. Pre-training in variable-specific bases captures the principal features of the target and achieves low (<0.05) total variation distance. The construction further extends naturally to higher-dimensional distributions of coupled variables, providing a route towards resource-efficient scaling of quantum generative models.
| Topic | Encoding and processing of data in quantum systems |
|---|---|
| Additional Topic | Hybrid quantum-classical approaches for learning and optimization |