Quantum Flow Matching

• URL: http://arxiv.org/abs/2508.12413v1
• Date: Sun, 17 Aug 2025 16:00:20 GMT
• Title: Quantum Flow Matching
• Authors: Zidong Cui, Pan Zhang, Ying Tang,
• Abstract summary: Quantum Flow Matching offers efficient interpolate between two density matrices.<n>QFM can be realized on a quantum computer without the need for costly circuit redesigns.
• Score: 8.09323038271377
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce Quantum Flow Matching (QFM)-a fully quantum-circuit realization that offers efficient interpolation between two density matrices. QFM offers systematic preparation of density matrices and generation of samples for accurately estimating observables, and can be realized on a quantum computer without the need for costly circuit redesigns. We validate its versatility on a set of applications: (i) generating target states with prescribed magnetization and entanglement entropy, (ii) estimating nonequilibrium free-energy differences to test the quantum Jarzynski equality, and (iii) expediting the study on superdiffusion breakdown. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.

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