Quantum Flow Matching
This work addresses the need for efficient generative modeling in quantum systems, offering a unifying framework for applications such as state preparation and nonequilibrium studies, though it is incremental as it adapts a classical paradigm to the quantum domain.
The authors tackled the problem of extending flow matching from classical to quantum generative modeling by introducing Quantum Flow Matching (QFM), a quantum-circuit method that efficiently interpolates between density matrices, enabling applications like generating target quantum states and estimating observables with systematic preparation.
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 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 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.