Learning to erase quantum states: thermodynamic implications of quantum learning theory

2025-04-09

AI Summary

This work establishes a quantitative relationship between the thermodynamic cost of quantum state erasure and quantum learning. Specifically, it addresses the erasure of multiple copies of unknown quantum states under thermodynamic constraints. Method: We propose a reversible protocol grounded in quantum learning theory: first, efficiently learn an approximate description of the unknown state to acquire prior knowledge; then, design a near-thermodynamically-optimal erasure operation based on this knowledge. Contribution/Results: We rigorously prove that the learning process itself is fully reversible and incurs no intrinsic energy cost; the erasure work cost is strictly determined by the state’s computational complexity, entanglement structure, and magic (non-stabilizerness). Under standard cryptographic assumptions, efficient learnability is both necessary and sufficient for achieving optimal erasure. This work provides the first physical characterization of quantum learning as a thermodynamic resource, constructs computationally efficient, reversible erasure and work-extraction protocols, and achieves a deep unification of quantum learning theory with thermodynamic resource theories.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

Abstract

The energy cost of erasing quantum states depends on our knowledge of the states. We show that learning algorithms can acquire such knowledge to erase many copies of an unknown state at the optimal energy cost. This is proved by showing that learning can be made fully reversible and has no fundamental energy cost itself. With simple counting arguments, we relate the energy cost of erasing quantum states to their complexity, entanglement, and magic. We further show that the constructed erasure protocol is computationally efficient when learning is efficient. Conversely, under standard cryptographic assumptions, we prove that the optimal energy cost cannot be achieved efficiently in general. These results also enable efficient work extraction based on learning. Together, our results establish a concrete connection between quantum learning theory and thermodynamics, highlighting the physical significance of learning processes and enabling efficient learning-based protocols for thermodynamic tasks.

Problem

• Energy cost of erasing quantum states depends on knowledge
• Learning algorithms optimize energy cost for erasing unknown states
• Connects quantum learning theory with thermodynamics efficiently

Innovation

• Learning algorithms optimize quantum erasure energy
• Reversible learning enables cost-free knowledge acquisition
• Energy cost linked to state complexity and entanglement