{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T23:02:44Z","timestamp":1778626964788,"version":"3.51.4"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T00:00:00Z","timestamp":1704672000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T00:00:00Z","timestamp":1704672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["NSTC 112-2119-M-033-001"],"award-info":[{"award-number":["NSTC 112-2119-M-033-001"]}],"id":[{"id":"10.13039\/100020595","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["NSTC 112-2119-M-033-001"],"award-info":[{"award-number":["NSTC 112-2119-M-033-001"]}],"id":[{"id":"10.13039\/100020595","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["NSTC 112-2119-M-033-001"],"award-info":[{"award-number":["NSTC 112-2119-M-033-001"]}],"id":[{"id":"10.13039\/100020595","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["NSTC 112-2119-M-033-001"],"award-info":[{"award-number":["NSTC 112-2119-M-033-001"]}],"id":[{"id":"10.13039\/100020595","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Quantum computing holds great potential for advancing the limitations of machine learning algorithms to handle higher dimensions of data and reduce overall training parameters in deep learning (DL) models. This study uses a trainable variational quantum circuit (VQC) on a gate-based quantum computing model to investigate the potential for quantum benefit in a model-free reinforcement learning problem. Through a comprehensive investigation and evaluation of the current model and capabilities of quantum computers, we designed and trained a novel hybrid quantum neural network based on the latest Qiskit and PyTorch framework. We compared its performance with a full-classical CNN with and without an incorporated VQC. Our research provides insights into the potential of deep quantum learning to solve a maze problem and, potentially, other reinforcement learning problems. We conclude that reinforcement learning problems can be practical with reasonable training epochs. Moreover, a comparative study of full-classical and hybrid quantum neural networks is discussed to understand these two approaches\u2019 performance, advantages, and disadvantages to deep Q-learning problems, especially on larger-scale maze problems larger than 4\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\times $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mo>\u00d7<\/mml:mo>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    4.\n                  <\/jats:p>","DOI":"10.1007\/s42484-023-00137-w","type":"journal-article","created":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T06:03:22Z","timestamp":1704693802000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Deep Q-learning with hybrid quantum neural network on solving maze problems"],"prefix":"10.1007","volume":"6","author":[{"given":"Hao-Yuan","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yen-Jui","family":"Chang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shih-Wei","family":"Liao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ching-Ray","family":"Chang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,1,8]]},"reference":[{"key":"137_CR1","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/s42484-022-00068-y","volume":"4","author":"N Dalla Pozza","year":"2022","unstructured":"Dalla Pozza N, Buffoni L, Martina S et al (2022) Quantum reinforcement learning: the maze problem. Quantum Mach Intell 4:11. https:\/\/doi.org\/10.1007\/s42484-022-00068-y","journal-title":"Quantum Mach Intell"},{"key":"137_CR2","doi-asserted-by":"publisher","first-page":"141007","DOI":"10.1109\/ACCESS.2020.3010470","volume":"8","author":"SY-C Chen","year":"2020","unstructured":"Chen SY-C, Yang C-HH, Qi J, Chen P-Y, Ma X, Goan H-S (2020) Variational quantum circuits for deep reinforcement learning. In IEEE access 8:141007\u2013141024. https:\/\/doi.org\/10.1109\/ACCESS.2020.3010470","journal-title":"In IEEE access"},{"key":"137_CR3","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/nature23474","volume":"549","author":"J Biamonte","year":"2017","unstructured":"Biamonte J, Wittek P, Pancotti N et al (2017) Quantum machine learning. Nature 549:195\u2013202. https:\/\/doi.org\/10.1038\/nature23474","journal-title":"Nature"},{"key":"137_CR4","unstructured":"Zhao C, Gao XS (2019) QDNN: DNN with quantum neural network layers. arXiv:1912.12660"},{"key":"137_CR5","unstructured":"Arthur D (2022) A hybrid quantum-classical neural network architecture for binary classification. arXiv:2201.01820"},{"key":"137_CR6","doi-asserted-by":"crossref","unstructured":"Schuld M (2021) Quantum machine learning models are kernel methods. arXiv:2101.11020","DOI":"10.1007\/978-3-030-83098-4_6"},{"issue":"1","key":"137_CR7","doi-asserted-by":"publisher","first-page":"808","DOI":"10.1038\/s41467-020-14454-2","volume":"11","author":"K Beer","year":"2020","unstructured":"Beer K, Bondarenko D, Farrelly T, Osborne TJ, Salzmann R, Scheiermann D, Wolf R (2020) Training deep quantum neural networks. Nat Commun 11(1):808. https:\/\/doi.org\/10.1038\/s41467-020-14454-2","journal-title":"Nat Commun"},{"key":"137_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TQCEBT54229.2022.10041479","volume":"2022","author":"S Lokes","year":"2022","unstructured":"Lokes S, Mahenthar CSJ, Kumaran SP, Sathyaprakash P, Jayakumar V (2022) Implementation of quantum deep reinforcement learning using variational quantum circuits, 2022 International conference on trends in quantum computing and emerging business technologies (TQCEBT). Pune, India 2022:1\u20134. https:\/\/doi.org\/10.1109\/TQCEBT54229.2022.10041479","journal-title":"Pune, India"},{"key":"137_CR9","unstructured":"Heimann D, Hohenfeld H, Wiebe F, Kirchner F (2022) Quantum deep reinforcement learning for robot navigation tasks. arXiv:2202.12180"},{"key":"137_CR10","doi-asserted-by":"publisher","first-page":"3913","DOI":"10.1038\/s41598-023-30990-5","volume":"13","author":"A Sannia","year":"2023","unstructured":"Sannia A, Giordano A, Gullo NL et al (2023) A hybrid classical-quantum approach to speed-up Q-learning. Sci Rep 13:3913. https:\/\/doi.org\/10.1038\/s41598-023-30990-5","journal-title":"Sci Rep"},{"key":"137_CR11","doi-asserted-by":"crossref","unstructured":"Kunczik L (2022) Quantum reinforcement learning-connecting reinforcement learning and quantum computing. In: Reinforcement learning with hybrid quantum approximation in the NISQ context. 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