Speaker
Description
A fundamental bottleneck holds back quantum machine learning: heuristic quantum methods cannot yet be meaningfully tested, since current hardware cannot run them at interesting scales. The train-classically, deploy-quantumly paradigm offers a seemingly impossible guarantee: the training objective is evaluated efficiently on a classical computer, while sampling from the trained model may remain classically intractable. We show this paradigm can yield genuinely universal quantum generative models, on two very different classically hard sampling models: the instantaneous quantum polynomial (IQP) quantum circuit Born machine (QCBM) and the boson sampling Born machine (BSBM). For the IQP-QCBM, we give the first universality result for the model class: $n$ hidden qubits make an $n$-qubit generator universal in the worst case. We also introduce adversarial kernel-adaptive training, proving it strictly more discriminative than the fixed Gaussian kernel, and validate it with up to 784 qubits. We then realize the same paradigm in a very different model of computation, introducing the BSBM: a boson sampler with trainable optical parameters. We establish that it can be trained classically w.r.t. wide families of MMD losses. Its bare form is not universal, but a fixed postprocessing map restores universality, and we construct a sequence of models whose expressivity grows monotonically to universality while provably retaining classical sampling hardness. Together, these results advance the theory of classically trained, quantum-deployed generative modeling across two models of computation.
| Topic | Quantum algorithms for machine learning applications |
|---|---|
| Additional Topic | Theoretical foundations of quantum learning |