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Classical Verification of Quantum Learning
Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data.
On the average-case complexity of learning output distributions of quantum circuits
In this work, we show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model.
A single $T$-gate makes distribution learning hard
We first show that the generative modelling problem associated with depth $d=n^{\Omega(1)}$ local quantum circuits is hard for any learning algorithm, classical or quantum.
Learnability of the output distributions of local quantum circuits
As many practical generative modelling algorithms use statistical queries -- including those for training quantum circuit Born machines -- our result is broadly applicable and strongly limits the possibility of a meaningful quantum advantage for learning the output distributions of local quantum circuits.
Quantum Computational Advantage via High-Dimensional Gaussian Boson Sampling
Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS.
Quantum Physics
