Conditional diffusion-based parameter generation for quantum approximate optimization algorithm

IF 5.6 2区 物理与天体物理 Q1 OPTICS
Fanxu Meng, Xiangzhen Zhou, Pengcheng Zhu, Yu Luo
{"title":"Conditional diffusion-based parameter generation for quantum approximate optimization algorithm","authors":"Fanxu Meng,&nbsp;Xiangzhen Zhou,&nbsp;Pengcheng Zhu,&nbsp;Yu Luo","doi":"10.1140/epjqt/s40507-025-00397-4","DOIUrl":null,"url":null,"abstract":"<div><p>The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm that shows promise in efficiently solving the Max-Cut problem, a representative example of combinatorial optimization. However, its effectiveness heavily depends on the parameter optimization pipeline, where the parameter initialization strategy is nontrivial due to the non-convex and complex optimization landscapes characterized by issues with low-quality local minima. Recent inspiration comes from the diffusion of classical neural network parameters, which has demonstrated that neural network training can benefit from generating good initial parameters through diffusion models. However, whether the diffusion model can enhance the parameter optimization and performance of QAOA by generating well-performing initial parameters is still an open topic. Therefore, in this work, we formulate the problem of finding good initial parameters as a generative task and propose the initial parameter generation scheme through dataset-conditioned pre-trained parameter sampling. Concretely, the generative machine learning model, specifically the denoising diffusion probabilistic model (DDPM), is trained to learn the distribution of pre-trained parameters conditioned on the graph dataset. Intuitively, the proposed framework aims to effectively distill knowledge from pre-trained parameters to generate well-performing initial parameters for QAOA. To benchmark our framework, we adopt trotterized quantum annealing (TQA)-based and graph neural network (GNN) prediction-based initialization protocols as baselines. Through numerical experiments on Max-Cut problem instances of various sizes, we show that conditional DDPM can consistently generate high-quality initial parameters, improve convergence to the approximation ratio, and exhibit greater robustness against local minima over baselines. Additionally, the experimental results also indicate that the conditional DDPM trained on small problem instances can be extrapolated to larger ones, thus demonstrating the extrapolation capacity of our framework in terms of the qubit number.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":"12 1","pages":""},"PeriodicalIF":5.6000,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-025-00397-4","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-025-00397-4","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm that shows promise in efficiently solving the Max-Cut problem, a representative example of combinatorial optimization. However, its effectiveness heavily depends on the parameter optimization pipeline, where the parameter initialization strategy is nontrivial due to the non-convex and complex optimization landscapes characterized by issues with low-quality local minima. Recent inspiration comes from the diffusion of classical neural network parameters, which has demonstrated that neural network training can benefit from generating good initial parameters through diffusion models. However, whether the diffusion model can enhance the parameter optimization and performance of QAOA by generating well-performing initial parameters is still an open topic. Therefore, in this work, we formulate the problem of finding good initial parameters as a generative task and propose the initial parameter generation scheme through dataset-conditioned pre-trained parameter sampling. Concretely, the generative machine learning model, specifically the denoising diffusion probabilistic model (DDPM), is trained to learn the distribution of pre-trained parameters conditioned on the graph dataset. Intuitively, the proposed framework aims to effectively distill knowledge from pre-trained parameters to generate well-performing initial parameters for QAOA. To benchmark our framework, we adopt trotterized quantum annealing (TQA)-based and graph neural network (GNN) prediction-based initialization protocols as baselines. Through numerical experiments on Max-Cut problem instances of various sizes, we show that conditional DDPM can consistently generate high-quality initial parameters, improve convergence to the approximation ratio, and exhibit greater robustness against local minima over baselines. Additionally, the experimental results also indicate that the conditional DDPM trained on small problem instances can be extrapolated to larger ones, thus demonstrating the extrapolation capacity of our framework in terms of the qubit number.

基于条件扩散的量子近似优化算法参数生成
量子近似优化算法(Quantum Approximate Optimization Algorithm, QAOA)是一种量子与经典的混合算法,在有效解决组合优化中的最大切问题方面表现出了很大的潜力。然而,其有效性在很大程度上取决于参数优化管道,其中参数初始化策略是非平凡的,因为非凸和复杂的优化景观以低质量的局部最小值问题为特征。最近的灵感来自经典神经网络参数的扩散,这表明神经网络训练可以从通过扩散模型生成良好的初始参数中获益。然而,扩散模型能否通过生成性能良好的初始参数来增强QAOA的参数优化和性能仍然是一个开放的话题。因此,在这项工作中,我们将寻找良好初始参数的问题制定为生成任务,并提出了通过数据集条件预训练参数采样的初始参数生成方案。具体来说,生成式机器学习模型,特别是去噪扩散概率模型(DDPM),被训练来学习基于图数据集的预训练参数的分布。直观地说,提出的框架旨在有效地从预训练参数中提取知识,以生成性能良好的QAOA初始参数。为了对我们的框架进行基准测试,我们采用了基于trotized quantum退火(TQA)和基于图神经网络(GNN)预测的初始化协议作为基准。通过对各种大小的Max-Cut问题实例的数值实验,我们表明条件DDPM可以始终如一地生成高质量的初始参数,提高收敛到近似比,并且对基线上的局部最小值表现出更强的鲁棒性。此外,实验结果还表明,在小问题实例上训练的条件DDPM可以外推到更大的问题实例,从而证明了我们的框架在量子比特数方面的外推能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
EPJ Quantum Technology
EPJ Quantum Technology Physics and Astronomy-Atomic and Molecular Physics, and Optics
CiteScore
7.70
自引率
7.50%
发文量
28
审稿时长
71 days
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following: Quantum measurement, metrology and lithography Quantum complex systems, networks and cellular automata Quantum electromechanical systems Quantum optomechanical systems Quantum machines, engineering and nanorobotics Quantum control theory Quantum information, communication and computation Quantum thermodynamics Quantum metamaterials The effect of Casimir forces on micro- and nano-electromechanical systems Quantum biology Quantum sensing Hybrid quantum systems Quantum simulations.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信