Speaker
Description
Sampling tasks have been successful in establishing quantum advantages, which has fueled research on using them for generative modeling. In particular, the potential to build generative models on classically hard distributions would immediately preclude classical simulability, due to theoretical separations. Implications of using such distributions on model trainability have, however, not been studied so far, which is a gap we close in this work.
We take three analytical types of probability distributions which we relate to product distributions, anticoncentrated distributions that are classically hard to sample from (e.g., IQP or Random Circuits), and peaked circuits. We study their (anti)concentration properties and implications on the concentration of commonly used loss functions as a proxy for trainability. Our results show that models built on distributions such as the ones found in problems showing quantum supremacy, concentrate and are therefore not trainable. In contrast, models outputting data from sparse distributions, such as peaked quantum circuits, do not suffer from exponentially concentrating losses, thus, can be trained.
We provide numerical results to showcase our analytical findings. We experiment with matrix product states, IQP circuits and peaked circuits and extrapolate to edge cases. We discuss our results in the context of verification of quantum processes, where they have been shown to require exponentially many samples.
Altogether, our results show that the requirements of sampling advantage, at least in the standard forms, are incompatible with trainability. We prove that quantum advantage can still be found, though its source must be distinct from anticoncentration.
| Topic | Quantum variational circuits and their applications |
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