[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117286-en":3,"doc-seo-117286-105":29,"detail-sidebar-cat-0-en-105":94},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},117286,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Improving 2–5 Qubit Quantum Phase Estimation Circuits Using Machine Learning","Quantum Phase Estimation (QPE) can estimate eigenvalue phases that are difficult for classical computation, but現有量子硬件的噪声会显著削弱效果。该研究通过在不同去极化噪声水平下仿真QPE电路来生成数据集：相位由相位门注入，并以随机选取的相位定义每个电路模型。对5种机器学习算法评估模型精度、预测速度、过拟合程度及误差随噪声变化，并与传统后处理方法对比。结果显示在4项指标上不存在单一“全能最优”，XGBoost在误差水平、预测时间与噪声下误差波动之间取得最佳折中；同时在IBMQ的2量子比特数据点上首次完成模型验证，最佳2量子比特模型相对实际相位误差≤2%，而传统方法误差约25%。","Air Force Institute of Technology  \nAFIT Scholar  \nFaculty Publications  \n5-15-2024  \nImproving 2–5 Qubit Quantum Phase Estimation Circuits Using Machine Learning  \nCharles Woodrum [*]  \nAir Force Institute of Technology  \nTorrey J. Wagner  \nAir Force Institute of Technology  \nDavid E. Weeks  \nAir Force Institute of Technology  \nFollow this and additional works at: [https://scholar.afit.edu/facpub](https://scholar.afit.edu/facpub)  \n Part of the Other Physics Commons, and the Theory and Algorithms Commons  \nRecommended Citation  \nWoodrum, C., Wagner, T., & Weeks, D. (2024) . Improving 2–5 qubit quantum phase estimation circuits using machine learning. Algorithms, 17(5), 214. [https://doi.org/10.3390/a17050214](https://doi.org/10.3390/a17050214)  \n[This Article is brought to you for free and open access by AFIT Scholar. It has been accepted for inclusion in](This Article is brought to you for free and open access by AFIT Scholar. It has been accepted for inclusion in)[ ](This Article is brought to you for free and open access by AFIT Scholar. It has been accepted for inclusion in)[Faculty Publications by an authorized administrator of AFIT Scholar. For more information](Faculty Publications by an authorized administrator of AFIT Scholar. For more information), please contact [AFIT.ENWL.Repository@us.af.mil](AFIT.ENWL.Repository@us.af.mil).  \n algorithms  \nArticle  \nImproving 2–5 Qubit Quantum Phase Estimation Circuits Using Machine Learning  \nCharles Woodrum 1,*, Torrey Wagner 1 and David Weeks 2  \nCitation: Woodrum, C.; Wagner, T.; Weeks, D. Improving 2–5 Qubit Quantum Phase Estimation Circuits Using Machine Learning. Algorithms 2024, 17, 214. [https://doi.org/](https://doi.org/)[ ](https://doi.org/)[10.3390/a17050214](10.3390/a17050214)  \nAcademic Editors: Hua-Lei Yin and Nan-Run Zhou  \nReceived: 15 March 2024  \nRevised: 10 May 2024  \nAccepted: 11 May 2024  \nPublished: 15 May 2024  \nCopyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Data Analytics Certificate Program, Graduate School of Engineering and Management, Air Force Institute of Technology, Wright-Patterson AFB, OH 45433, USA; [torrey.wagner.2@us.af.mil](torrey.wagner.2@us.af.mil)  \n2 Department of Engineering Physics, Graduate School of Engineering and Management, Air Force Institute of Technology, Wright-Patterson AFB, OH 45433, USA; [david.weeks@afit.edu](david.weeks@afit.edu)  \n* [Correspondence: woodrum.27@osu.edu](Correspondence: woodrum.27@osu.edu)  \nAbstract: Quantum computing has the potential to solve problems that are currently intractable to classical computers with algorithms like Quantum Phase Estimation (QPE); however, noise significantly hinders the performance of today’s quantum computers. Machine learning has the potential to improve the performance of QPE algorithms, especially in the presence of noise. In this work, QPE circuits were simulated with varying levels of depolarizing noise to generate datasets of QPE output. In each case, the phase being estimated was generated with a phase gate, and each circuit modeled was defined by a randomly selected phase. The model accuracy, prediction speed, overfitting level and variation in accuracy with noise level was determined for 5 machine learning algorithms. These attributes were compared to the traditional method of post-processing and a 6x–36 improvement in model performance was noted, depending on the dataset. No algorithm was a clear winner when considering these 4 criteria, as the lowest-error model (neural network) was also the slowest predictor; the algorithm with the lowest overfitting and fastest prediction time (linear regression) had the highest error level and a high degree of variation","cbCailRRDjdc8C2B","https://ap.wps.com/l/cbCailRRDjdc8C2B","pdf",2024918,1,18,"English","en",105,"# Introduction\n## Quantum Phase Estimation background\n# Machine Learning Approach for QPE\n## Dataset generation with depolarizing noise\n## Model evaluation criteria\n# Results and Comparison\n## Performance vs traditional post-processing\n## Tradeoffs among algorithms\n# Experimental Validation","[{\"question\":\"为什么需要在QPE中引入机器学习？\",\"answer\":\"噪声显著降低当前量子计算机上QPE的效果。机器学习被用于在噪声存在时提升QPE算法的表现。\"},{\"question\":\"研究如何生成用于训练与评估的数据集？\",\"answer\":\"在不同去极化噪声水平下仿真QPE电路，使用相位门生成被估计相位，并为每个电路随机选择相位以形成数据集。\"},{\"question\":\"哪种机器学习算法表现最好，依据是什么？\",\"answer\":\"综合误差水平、预测时间和噪声下误差波动，XGBoost被认为在权衡四项标准上取得最佳折中；但在4个标准同时考虑时没有单一算法始终最优。\"},{\"question\":\"2量子比特的实测验证结果如何？\",\"answer\":\"基于IBM Q的2量子比特数据点验证时，最佳2量子比特模型可在实际相位的2%以内完成预测，而传统方法误差约为25%。\"}]",1785675009,45,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":89,"head_meta":91,"extra_data":93,"updated_unix":27},"improving-25-qubit-quantum-phase-estimation-circuits-using-machine-learning","",{"@graph":35,"@context":88},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/improving-25-qubit-quantum-phase-estimation-circuits-using-machine-learning/117286/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80,84],{"name":71,"@type":72,"acceptedAnswer":73},"为什么需要在QPE中引入机器学习？","Question",{"text":74,"@type":75},"噪声显著降低当前量子计算机上QPE的效果。机器学习被用于在噪声存在时提升QPE算法的表现。","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"研究如何生成用于训练与评估的数据集？",{"text":79,"@type":75},"在不同去极化噪声水平下仿真QPE电路，使用相位门生成被估计相位，并为每个电路随机选择相位以形成数据集。",{"name":81,"@type":72,"acceptedAnswer":82},"哪种机器学习算法表现最好，依据是什么？",{"text":83,"@type":75},"综合误差水平、预测时间和噪声下误差波动，XGBoost被认为在权衡四项标准上取得最佳折中；但在4个标准同时考虑时没有单一算法始终最优。",{"name":85,"@type":72,"acceptedAnswer":86},"2量子比特的实测验证结果如何？",{"text":87,"@type":75},"基于IBM Q的2量子比特数据点验证时，最佳2量子比特模型可在实际相位的2%以内完成预测，而传统方法误差约为25%。","https://schema.org",{"og:url":51,"og:type":90,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":92,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":95},[96,100,104,108,113,118,123,126,131,134,138],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":105,"show_sort_weight":106,"slug":107},"Exam",70,"exam",{"id":109,"doc_module":4,"doc_module_name":45,"category_name":110,"show_sort_weight":111,"slug":112},5,"Comic",60,"comic",{"id":114,"doc_module":4,"doc_module_name":45,"category_name":115,"show_sort_weight":116,"slug":117},6,"Technology",50,"technology",{"id":119,"doc_module":4,"doc_module_name":45,"category_name":120,"show_sort_weight":121,"slug":122},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":124,"slug":125},30,"research-report",{"id":127,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":129,"slug":130},9,"Religion & Spirituality",20,"religion-spirituality",{"id":129,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":129,"slug":133},"World Cup","world-cup",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":135,"slug":137},10,"Lifestyle","lifestyle",{"id":139,"doc_module":4,"doc_module_name":45,"category_name":140,"show_sort_weight":109,"slug":141},19,"General","general"]