发表机构
Keio University; Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q); Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC); University of California, Berkeley（庆应义塾大学; 人类生物学-微生物组-量子研究中心（WPI-Bio2Q）; 庆应义塾大学可持续量子人工智能中心（KSQAIC）; 加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出Quantum MeanFlow（QMF），一种支持单步量子生成采样的方法，在MNIST数据集上验证其性能优于单步量子流匹配（QFM），可减少量子电路评估次数。
AI 中文摘要
量子生成模型为探究量子计算是否能增强生成式机器学习提供了有前景的框架。Flow matching是一种生成方法，通过学习到的速度场将简单的已知分布迁移至目标数据分布来生成样本。其量子对应版本即量子流匹配（quantum flow matching, QFM）于近期提出，与经典版本类似，在推理过程中需要对常微分方程进行多时间步积分。由于每个时间步都依赖前一步的输出，电路提交是串行的，这对量子计算机而言存在输入输出成本高的缺陷。为缓解该问题，我们提出Quantum MeanFlow（QMF），即MeanFlow公式的量子对应版本，支持单步样本生成。QFM在每个时间步学习瞬时速度场，而QMF学习时间区间内的平均速度。我们使用参数化量子电路学习这些速度场，并在MNIST数据集上对两种方法进行基准测试。结果显示，尽管单步QMF的图像质量低于多步QFM，但在每个采样次数下，其性能均优于单步QFM采样。我们的两种模型均在IBM量子计算机上执行，最优N次拒绝采样可在不修改电路的情况下恢复大部分因设备噪声损失的准确率，这对QMF尤为有利，因为其每张图像仅需一次电路评估。在此，我们确立QMF为一种可行的单步量子生成采样方法，减少了每张生成样本所需的量子电路评估次数。
英文摘要
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.
Comments17 pages, 6 figures
