Quantum equilibrium propagation for efficient training of quantum systems based on Onsager reciprocity

Area of Science:

• Quantum Computing
• Artificial Intelligence
• Neuromorphic Hardware

Background:

• Machine learning and AI drive demand for energy-efficient hardware.
• Neuromorphic systems offer alternative hardware but lack efficient training methods.
• Equilibrium propagation (EP) is a studied training approach for classical energy-based models.

Purpose of the Study:

• To derive a quantum version of equilibrium propagation (EP).
• To enable efficient, physics-based training for quantum neuromorphic systems.
• To extract training gradients for arbitrary quantum systems via linear response experiments.

Main Methods:

• Established a connection between EP and Onsager reciprocity.
• Derived a quantum version of EP applicable to arbitrary quantum systems.
• Utilized linear response experiments to extract training gradients.

Main Results:

• Introduced Quantum EP for training quantum systems.
• Demonstrated gradient extraction via a single linear response experiment.
• Illustrated applications in quantum phase discovery, sensing, and phase boundary exploration.

Conclusions:

• Quantum EP provides an efficient training approach for quantum neuromorphic hardware.
• This method can address classically intractable problems like quantum phase discovery.
• The scheme is compatible with various quantum simulation platforms.