mlsanityData to 7 Oct 2026

Quantum Flow Matching

arXiv 2508.12413 ↗First posted 17 Aug 2025quant-ph cs.AI cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 71 references that are in the map. First posted on arXiv 17 Aug 2025.

Builds on

14 of 71 references.

References · 14

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2022Flow Matching for Generative Modelingcited by 5,426
  6. 2015Variational Inference with Normalizing Flowscited by 2,161
  7. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  8. 2020Power of data in quantum machine learningcited by 336
  9. 2023Error Bounds for Flow Matching Methodscited by 88
  10. 2022Out-of-distribution generalization for learning quantum dynamicscited by 49
  11. 2025Variational Rectified Flow Matchingcited by 34
  12. 2023Generative quantum machine learning via denoising diffusion probabilistic modelscited by 30
2 more
  1. 2025Local Diffusion Models and Phases of Data Distributionscited by 8
  2. 2024BOSS: Blocking algorithm for optimizing shuttling scheduling in Ion Trapcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transportcited by 0
  2. 2026Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensionscited by 0
  3. 2026Quantum MeanFlow: single-shot generative sampling on NISQ hardwarecited by 0
  4. 2026Conditional Quantum Flow Matching for Data-Scarce Physiological Signal Augmentationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Generative Modeling of Quantum Distribution with Functional Flow Matching
  2. 2025Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models
  3. 2025Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion
  4. 2023Quantum-Noise-Driven Generative Diffusion Models
  5. 2024Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble
  6. 2026Scalable quantum simulation of continuous-time generative models via tensor networks
  7. 2026An Hybrid Quantum-Classical Diffusion Model for Image Generation
  8. 2023Quantum circuit synthesis with diffusion models