Power of data in quantum machine learning.

Area of Science:

• Quantum computing
• Machine learning
• Computational complexity

Background:

• Quantum computing offers potential for machine learning (ML).
• ML tasks with data differ from standard computational problems.
• Classical algorithms may struggle with certain complex computations.

Purpose of the Study:

• Develop a methodology to assess quantum advantage in ML.
• Analyze the performance of classical ML against quantum ML.
• Propose a quantum model for potential speed-up.

Main Methods:

• Utilizing rigorous prediction error bounds.
• Developing a framework for assessing learning task advantage.
• Implementing and testing projected quantum models.
• Conducting large-scale numerical simulations for gate-based quantum ML.

Main Results:

• Classical ML can predict classically hard problems from data.
• Prediction error bounds are asymptotically tight and empirically predictive.
• Classical ML models demonstrate competitiveness with quantum models.
• A projected quantum model shows rigorous speed-up in the fault-tolerant regime.
• Significant prediction advantage observed for near-term quantum implementations on engineered datasets.

Conclusions:

• Data-driven classical ML can rival specialized quantum approaches.
• Quantum advantage in ML requires careful consideration of data.
• Projected quantum models offer a path to quantum speed-up.
• Near-term quantum ML shows promise on specific tasks and datasets.