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Quantum Flow Matching
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The 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 the Quantum Flow Matching (QFM), a 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 quantum computers 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. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.
Forward citations
Cited by 2 Pith papers
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Stochastic Schr\"odinger Equations for Quantum Reverse Diffusion
Exact reverse stochastic Schrödinger equations for continuously monitored Pauli channels recover the initial pure state almost surely, with an approximate extension to depolarizing noise.
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Quantum Reversibility Meets Classical Reverse Diffusion
The semiclassical limit of the Petz-reversed Lindblad equation reproduces the Bayes-rule reverse-time diffusion equation, with the reference state's Wigner function playing the role of the classical score distribution.
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