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Barren Plateaus Preclude Learning Scramblers.
Zoë Holmes1, Andrew Arrasmith2, Bin Yan2,3
1Information Sciences, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Physical Review Letters
|May 28, 2021
Summary
Quantum machine learning (QML) cannot efficiently learn unknown scrambling processes due to barren plateaus, which cause exponentially vanishing gradients. This finding limits the application of QML in quantum chaos and thermalization research.
Area of Science:
- Quantum Information Science
- Quantum Machine Learning
- Condensed Matter Theory
Background:
- Scrambling processes rapidly spread quantum entanglement in many-body systems.
- Investigating scrambling is crucial for understanding quantum chaos and thermalization.
- Standard techniques struggle to analyze these complex quantum dynamics.
Purpose of the Study:
- To determine if quantum machine learning (QML) can effectively study quantum scrambling processes.
- To identify fundamental limitations of QML in learning unknown unitary dynamics.
Main Methods:
- Proving a no-go theorem for QML-based learning of scrambling.
- Analyzing the landscape of cost functions for variational quantum algorithms.
- Numerical and analytical investigations of approximate scramblers.
Main Results:
- A no-go theorem demonstrates that QML likely faces barren plateaus for scrambling.
- Barren plateaus lead to exponentially vanishing cost gradients with system size.
- This implies exponential resource scaling, negating common mitigation strategies.
Conclusions:
- Generic limits exist on the learnability of unknown unitaries using QML.
- The study highlights challenges for QML in quantum chaos and thermalization.
- Prior information is essential for successful QML application to scrambling.
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