Quantum MeanFlow: single-shot generative sampling on NISQ hardware
Abstract
Quantum generative models offer a promising framework for exploring whether quantum computation can enhance generative machine learning. Flow matching is a generative method in which samples are generated by transporting a simple, known distribution to the target data distribution with a learned velocity field. Its quantum counterpart, known as quantum flow matching (QFM), was introduced recently, and, like its classical counterpart, requires integrating an ordinary differential equation over many time steps during inference. As each step requires the output from the previous step, the circuit submission is sequential and a drawback on quantum computers as they have high input/output costs. To alleviate this problem, we introduce Quantum MeanFlow (QMF), the quantum analogue of the MeanFlow formulation, which allows single-step sample generation. While the QFM learns an instantaneous velocity field at each time step, QMF learns the average velocity over a time interval. We use a parameterized quantum circuit to learn these velocity fields and benchmark the two methods on the MNIST dataset. We show that while single-step QMF has lower image quality compared to multi-step QFM, it performs better than the single-step QFM sampling at every shot count. Both of our models are executed on IBM quantum computers and best-of-N rejection sampling recovers most of the accuracy lost to device noise without modifying the circuit. This is especially advantageous for QMF which has only one circuit evaluation per image. Here, We establish QMF as a viable method for single-step quantum generative sampling, saving on quantum circuit evaluations per generated sample.
Related
- Hardware-Efficient Error Mitigation and Shot-Efficient Sampling on IBM Quantum Hardware
- Hardware Demonstration of Neural-Surrogated Quantum-Enhanced MCMC for Large-Scale Constrained Boltzmann Sampling
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- On Certifying Source Sampling Hardness in Quantum Generative Modeling
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BibTeX
@misc{joshi2026quantum,
title = {{Quantum MeanFlow: single-shot generative sampling on NISQ hardware}},
author = {Ashish Joshi and Eshaan Mistry and Takahiko Koyama},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02186},
eprint = {2609.02186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02186},
}
RIS
TY - UNPB
TI - Quantum MeanFlow: single-shot generative sampling on NISQ hardware
AU - Ashish Joshi
AU - Eshaan Mistry
AU - Takahiko Koyama
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02186
UR - https://arxiv.org/abs/2609.02186
AB - Quantum generative models offer a promising framework for exploring whether quantum computation can enhance generative machine learning. Flow matching is a generative method in which samples are generated by transporting a simple, known distribution to the target data distribution with a learned velocity field. Its quantum counterpart, known as quantum flow matching (QFM), was introduced recently, and, like its classical counterpart, requires integrating an ordinary differential equation over many time steps during inference. As each step requires the output from the previous step, the circuit submission is sequential and a drawback on quantum computers as they have high input/output costs. To alleviate this problem, we introduce Quantum MeanFlow (QMF), the quantum analogue of the MeanFlow formulation, which allows single-step sample generation. While the QFM learns an instantaneous velocity field at each time step, QMF learns the average velocity over a time interval. We use a parameterized quantum circuit to learn these velocity fields and benchmark the two methods on the MNIST dataset. We show that while single-step QMF has lower image quality compared to multi-step QFM, it performs better than the single-step QFM sampling at every shot count. Both of our models are executed on IBM quantum computers and best-of-N rejection sampling recovers most of the accuracy lost to device noise without modifying the circuit. This is especially advantageous for QMF which has only one circuit evaluation per image. Here, We establish QMF as a viable method for single-step quantum generative sampling, saving on quantum circuit evaluations per generated sample.
ER -