Quantum Flow Matching

2025/08/17 by Zidong Cui, Pan Zhang, Cui, Zidong +3 · 1 voice · 2 citations
Computer Science · Physics and Astronomy · #Cloud Computing and Resource Management #Data Stream Mining Techniques #cs.AI #cs.LG #quant-ph

paper · pdf · doi:10.48550/arxiv.2508.12413

arxiv published 2025/08/17 · arxiv updated 2026/06/30

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.

Citations

• Measurement-Based Quantum Diffusion Models
• Local Diffusion Models and Phases of Data Distributions
• Correcting a noisy quantum computer using a quantum computer
• Simulating dynamics of correlated matter with neural quantum states
• Generative Decoding for Quantum Error-correcting Codes
• Variational quantum thermalizers based on weakly-symmetric nonunitary multi-qubit operations
• Variational Rectified Flow Matching
• Establishing a New Benchmark in Quantum Computational Advantage with 105-qubit Zuchongzhi 3.0 Processor
• BOSS: Blocking algorithm for optimizing shuttling scheduling in Ion Trap
• Quantum error correction below the surface code threshold
• Beyond-classical computation in quantum simulation
• Error Bounds for Flow Matching Methods
• Flow Matching for Generative Modeling
• Learning nonequilibrium statistical mechanics and dynamical phase transitions
• High-Resolution Image Synthesis with Latent Diffusion Models
• High-Resolution Image Synthesis with Latent Diffusion Models
• Computing Free Energies with Fluctuation Relations on Quantum Computers
• Score-Based Generative Modeling through Stochastic Differential Equations
• Denoising Diffusion Implicit Models
• Denoising Diffusion Probabilistic Models
• Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits
• Machine learning and the physical sciences
• Strategies for quantum computing molecular energies using the unitary\n coupled cluster ansatz
• From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
• Variational Inference with Normalizing Flows
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Jarzynski Relations for Quantum Systems and Some Applications
• A Quantum Fluctuation Theorem

Cited by

• Exact Stochastic Differential Equations for Quantum Reverse Diffusion
• Quantum Reversibility Meets Classical Reverse Diffusion
• Measurement-Based Quantum Diffusion Models

Discussions

• Flow matching has become a dominant paradigm in generative modeling. We develop Quantum Flow Matching, with diverse applications: generate states with target magnetization and entanglement entropy; pr [bsky, 4 points, 0 comments]

Related

• Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models
• Flowing Through Hilbert Space: Quantum-Enhanced Generative Models for Lattice Field Theory
• Resource-adaptive quantum flow algorithms for quantum simulations of many-body systems: sub-flow embedding procedures
• Quantum flow algorithms for simulating many-body systems on quantum computers
• Q-Flow: Generative Modeling for Differential Equations of Open Quantum Dynamics with Normalizing Flows