Quantum Flow Matching

TL;DR

Quantum Flow Matching (QFM) extends classical flow matching to quantum systems, enabling efficient density matrix interpolation, state preparation, and observable estimation on quantum computers, with diverse applications demonstrated.

Contribution

Introduces Quantum Flow Matching, a novel quantum-circuit framework for efficient density matrix interpolation and state generation, unifying quantum generative modeling methods.

Findings

Successfully generates target quantum states with specific properties.

Accurately estimates nonequilibrium free-energy differences.

Accelerates research on superdiffusion phenomena.

Abstract

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.