Quantum score matching with applications to learning thermal states
Quantum score matching learns Gibbs states optimally at high temperature and runs on IBM hardware.
The paper introduces a quantum score-matching framework for learning from density operators, including circuit implementations and theoretical guarantees. Applied to Gibbs-state learning, it avoids additional thermal-state preparation and claims information-theoretically optimal sample complexity in the high-temperature regime for Hamiltonians with bounded locality and interaction degree. Simulations remained effective when gradients were estimated inaccurately under limited measurement budgets. On IBM quantum hardware, without error mitigation or correction, relative Hamiltonian-parameter error fell from 64% to approximately 10%.
- Framework extends score matching to noncommuting quantum density operators.
- Gibbs learning avoids extra thermal-state preparation in the high-temperature regime.
- Theory claims optimal sample complexity for bounded-locality Hamiltonians.
- IBM hardware cut parameter error from 64% to about 10% without mitigation.
From the original article
1 min read at arxiv.orgScore matching has driven major advances in classical generative learning by enabling models to learn from data without evaluating intractable normalization constants, or partition functions. Yet, extending this principle to quantum learning requires rethinking its foundations, as quantum states are described by noncommuting density operators rather than scalar probabilities.
By Yulong Dong · arxiv.org
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