Provably Trainable Rotationally Equivariant Quantum Machine Learning

Understand

Exploiting the power of quantum computation to realise superior machine learning algorithmshas been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical challenges.

• A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes -- large regions where cost function gradients vanish exponentially in the number of qubits employed, rendering large models effectively untrainable.
• A leading strategy for combating this effect is to build problem-specific models which take into account the symmetries of their data in order to focus on a smaller, relevant subset of Hilbert space.
• In this work, we introduce a family of rotationally equivariant QML models built upon the quantum Fourier transform, and leverage recent insights from the Lie-algebraic study of QML models to prove that (a subset of) our models do not exhibit barren plateaus.