Limits of quantum generative models with classical sampling hardness
This work addresses the challenge of achieving quantum advantage in generative modeling for quantum computing researchers, revealing a trade-off that limits practical applications and is incremental in refining theoretical understanding.
The paper tackles the problem of training quantum generative models on classically hard distributions, showing that models with anticoncentrated outputs are not trainable on average, while those with sparse outputs can be trained, leading to potential classical simulability.
Sampling tasks have been successful in establishing quantum advantages both in theory and experiments. This has fueled the use of quantum computers for generative modeling to create samples following the probability distribution underlying a given dataset. In particular, the potential to build generative models on classically hard distributions would immediately preclude classical simulability, due to theoretical separations. In this work, we study quantum generative models from the perspective of output distributions, showing that models that anticoncentrate are not trainable on average, including those exhibiting quantum advantage. In contrast, models outputting data from sparse distributions can be trained. We consider special cases to enhance trainability, and observe that this opens the path for classical algorithms for surrogate sampling. This observed trade-off is linked to verification of quantum processes. We conclude that quantum advantage can still be found in generative models, although its source must be distinct from anticoncentration.