Inference, interference and invariance: How the Quantum Fourier Transform can help to learn from data

Understand

How can we take inspiration from a typical quantum algorithm to design heuristics for machine learning? A common blueprint, used from Deutsch-Josza to Shor's algorithm, is to place labeled information in superposition via an oracle, interfere in Fourier space, and measure.

• In this paper, we want to understand how this interference strategy can be used for inference, i.e.
• to generalize from finite data samples to a ground truth.
• Our investigative framework is built around the Hidden Subgroup Problem (HSP), which we transform into a learning task by replacing the oracle with classical training data.