Sample Efficient Inference of Quantum Data

Quantum data processing is a natural application of quantum machine learning (QML), where the learning algorithm can directly access the exponential complexity of the input state without suffering from the overhead associated with encoding classical data in the quantum domain. Here we present an analytical framework for finding the optimal conditions to reconstruct an arbitrary set of observables of a quantum state by means of a continuous interaction in a larger Hilbert space and local measurements. We also study the sample efficiency of full state reconstruction, generalising the expressive capacity framework [1] to static quantum data. In particular we assess the optimality of the quantum channel that drives the evolution by showcasing how it explicitly affects the condition number of the tomographic inversion map.

[1] Hu et al, Phys. Rev. X 13, 041020 (2022)