Learning in Finitely-Sampled Quantum Systems 2: Applications*

Machine learning in quantum systems has been hindered by the emergence of “barren plateaus” which preclude training, particularly in the presence of sampling noise, and are associated with increasing expressibility - defined as a distance from a 2-design.  Here we present a practical method for learning in finitely-sampled qubit systems based instead on the expressive capacity analysis from part 1. This capacity metric encompasses the input-distribution, algorithm, physical device, and measurement - ideal for a full-stack analysis of current quantum platforms and informing ansatz design tailored to a specific system.  We describe the construction of optimal computational-basis measurements that are robust to sampling noise, providing a compressed representation of the quantum feature space and a powerful learning method inspired by quantum reservoir computing which is not subject to barren plateaus. We demonstrate this approach on parameterized quantum circuits experimentally realized on an IBM superconducting qubit processor, emphasizing how one naturally obtains principal features unique to a given system and its particular noise environment.  Using very limited measurement resources we are able to reliably estimate device principal features, and connect capacity with performance on learning tasks.