Speaker
Description
Quantum computers can sample from probability distributions believed to be classically intractable, providing a foundation for quantum generative modeling. Training such models, rather than their expressivity, has emerged as the central bottleneck. Gradient estimation by parameter-shift or finite-difference methods requires separate circuit executions for each parameter, a cost amplified by finite-shot noise and barren plateaus, and quantum circuit models admit no backpropagation mechanism that computes all gradients in a single pass. Quantum Boltzmann machines (QBMs) are expressive generative models, but existing training methods estimate one expectation value per Hamiltonian term and require explicit access to target data probabilities, so no QBM has been trained from data samples alone. We introduce a generalized contrastive divergence algorithm for training quantum models. For semi-quantum restricted Boltzmann machines, we derive the conditional probabilities of the Gibbs state in closed form and give a general recipe for the quantum circuits that generate the samples needed for each parameter update. The resulting update rule is estimated from data and model samples alone, without access to the explicit data distribution, at a cost of O(1) forward passes per step independent of the number of parameters, in analogy with classical backpropagation. Numerical simulations on discretized Gaussian, bars-and-stripes, and Tetris targets show that the method matches the accuracy of likelihood-based training while requiring orders of magnitude fewer samples. Our approach provides a scalable route to training expressive quantum generative models directly on quantum hardware.
| Topic | Hybrid quantum-classical approaches for learning and optimization |
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| Additional Topic | Quantum algorithms for machine learning applications |