Out-of-distribution generalization for learning quantum dynamics

Area of Science:

• Quantum Machine Learning
• Quantum Computing Theory
• Generalization Bounds

Background:

• Generalization bounds are crucial for understanding data needs in Quantum Machine Learning (QML).
• Existing QML research guarantees in-distribution generalization for quantum neural networks (QNNs).
• Out-of-distribution (OOD) generalization in QML remains an open challenge, limiting model applicability to unseen data distributions.

Purpose of the Study:

• To establish theoretical guarantees for out-of-distribution generalization in Quantum Machine Learning.
• To demonstrate the ability to learn unknown quantum unitaries from data generated from different distributions.
• To explore the implications for near-term quantum hardware and quantum circuit compilation.

Main Methods:

• Theoretical analysis of generalization bounds for quantum models.
• Proving out-of-distribution generalization for the specific task of learning an unknown unitary.
• Utilizing product states for training and evaluating generalization on entangled states.

Main Results:

• The study proves out-of-distribution generalization for learning an unknown unitary in QML.
• It is demonstrated that a quantum model trained on product states can learn the action of a unitary on entangled states.
• This theoretical advancement is achieved without requiring training data from the target distribution.

Conclusions:

• This work bridges the gap in understanding OOD generalization for QML.
• The findings suggest that learning quantum dynamics is feasible on near-term quantum hardware using simpler training states.
• The results offer new avenues for classical and quantum circuit compilation strategies.