Efficient learnability of 3D shallow-circuit states

Determine whether quantum states prepared by shallow geometrically-local quantum circuits acting on 3D lattices (or more general geometries) can be learned efficiently, by developing algorithms with polynomial-time (or otherwise rigorously bounded) classical computational complexity and quantifying the required sample complexity.

Background

The authors present an efficient algorithm for learning states prepared by shallow circuits on 2D lattices, leveraging disentangling techniques and 1D constraint satisfaction. Extending these techniques beyond 2D introduces additional challenges due to the complexity of higher-dimensional constraints.

This problem asks whether analogous efficient learning guarantees can be established for 3D lattices or even more general geometries, matching the 2D results in computational and sample efficiency.