{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T04:14:18Z","timestamp":1775880858590,"version":"3.50.1"},"reference-count":55,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T00:00:00Z","timestamp":1692835200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T00:00:00Z","timestamp":1692835200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"crossref","award":["DP210102831"],"award-info":[{"award-number":["DP210102831"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2023,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Machine learning is among the most widely anticipated use cases for near-term quantum computers, however there remain significant theoretical and implementation challenges impeding its scale up. In particular, there is an emerging body of work which suggests that generic, data agnostic quantum machine learning (QML) architectures may suffer from severe trainability issues, with the gradient of typical variational parameters vanishing exponentially in the number of qubits. Additionally, the high expressibility of QML models can lead to overfitting on training data and poor generalisation performance. A promising strategy to combat both of these difficulties is to construct models which explicitly respect the symmetries inherent in their data, so-called geometric quantum machine learning (GQML). In this work, we utilise the techniques of GQML for the task of image classification, building new QML models which are equivariant with respect to reflections of the images. We find that these networks are capable of consistently and significantly outperforming generic ansatze on complicated real-world image datasets, bringing high-resolution image classification via quantum computers closer to reality. Our work highlights a potential pathway for the future development and implementation of powerful QML models which directly exploit the symmetries of data.<\/jats:p>","DOI":"10.1088\/2632-2153\/acf096","type":"journal-article","created":{"date-parts":[[2023,8,15]],"date-time":"2023-08-15T22:44:31Z","timestamp":1692139471000},"page":"035027","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":39,"title":["Reflection equivariant quantum neural networks for enhanced image classification"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4500-3139","authenticated-orcid":true,"given":"Maxwell","family":"T West","sequence":"first","affiliation":[]},{"given":"Martin","family":"Sevior","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3476-2348","authenticated-orcid":false,"given":"Muhammad","family":"Usman","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2023,8,24]]},"reference":[{"key":"mlstacf096bib1","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/nature23474","article-title":"Quantum machine learning","volume":"549","author":"Biamonte","year":"2017","journal-title":"Nature"},{"key":"mlstacf096bib2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-020-14454-2","article-title":"Training deep quantum neural networks","volume":"11","author":"Beer","year":"2020","journal-title":"Nat. Commun."},{"key":"mlstacf096bib3","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1038\/s41586-019-0980-2","article-title":"Supervised learning with quantum-enhanced feature spaces","volume":"567","author":"Havl\u00ed\u010dek","year":"2019","journal-title":"Nature"},{"key":"mlstacf096bib4","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/aa8072","article-title":"Quantum autoencoders for efficient compression of quantum data","volume":"2","author":"Romero","year":"2017","journal-title":"Quantum Sci. Technol."},{"key":"mlstacf096bib5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.012324","article-title":"Quantum generative adversarial networks","volume":"98","author":"Dallaire-Demers","year":"2018","journal-title":"Phys. Rev. A"},{"key":"mlstacf096bib6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.1.033063","article-title":"Continuous-variable quantum neural networks","volume":"1","author":"Killoran","year":"2019","journal-title":"Phys. Rev. Res."},{"key":"mlstacf096bib7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.040504","article-title":"Quantum machine learning in feature Hilbert spaces","volume":"122","author":"Schuld","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"mlstacf096bib8","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1038\/s41567-019-0648-8","article-title":"Quantum convolutional neural networks","volume":"15","author":"Cong","year":"2019","journal-title":"Nat. Phys."},{"key":"mlstacf096bib9","article-title":"Supervised quantum machine learning models are kernel methods","author":"Schuld","year":"2021"},{"key":"mlstacf096bib10","article-title":"Hybrid quantum-classical generative adversarial network for high resolution image generation","author":"Tsang","year":"2022"},{"key":"mlstacf096bib11","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1038\/s42256-023-00661-1","article-title":"Towards quantum enhanced adversarial robustness in machine learning","volume":"5","author":"West","year":"2023","journal-title":"Nat. Mach. Intell."},{"key":"mlstacf096bib12","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1038\/s41567-021-01287-z","article-title":"A rigorous and robust quantum speed-up in supervised machine learning","volume":"17","author":"Liu","year":"2021","journal-title":"Nat. Phys."},{"key":"mlstacf096bib13","doi-asserted-by":"publisher","first-page":"1182","DOI":"10.1126\/science.abn7293","article-title":"Quantum advantage in learning from experiments","volume":"376","author":"Huang","year":"2022","journal-title":"Science"},{"key":"mlstacf096bib14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.5.023186","article-title":"Benchmarking adversarially robust quantum machine learning at scale","volume":"5","author":"West","year":"2023","journal-title":"Phys. Rev. Res."},{"key":"mlstacf096bib15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-018-07090-4","article-title":"Barren plateaus in quantum neural network training landscapes","volume":"9","author":"McClean","year":"2018","journal-title":"Nat. Commun."},{"key":"mlstacf096bib16","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.3.010313","article-title":"Connecting ansatz expressibility to gradient magnitudes and barren plateaus","volume":"3","author":"Holmes","year":"2022","journal-title":"PRX Quantum"},{"key":"mlstacf096bib17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-021-21728-w","article-title":"Cost function dependent barren plateaus in shallow parametrized quantum circuits","volume":"12","author":"Cerezo","year":"2021","journal-title":"Nat. Commun."},{"key":"mlstacf096bib18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-021-27045-6","article-title":"Noise-induced barren plateaus in variational quantum algorithms","volume":"12","author":"Wang","year":"2021","journal-title":"Nat. Commun."},{"key":"mlstacf096bib19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.11.041011","article-title":"Absence of barren plateaus in quantum convolutional neural networks","volume":"11","author":"Pesah","year":"2021","journal-title":"Phys. Rev. X"},{"key":"mlstacf096bib20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.3.033090","article-title":"Entanglement devised barren plateau mitigation","volume":"3","author":"Patti","year":"2021","journal-title":"Phys. Rev. Res."},{"key":"mlstacf096bib21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42484-020-00036-4","article-title":"Layerwise learning for quantum neural networks","volume":"3","author":"Skolik","year":"2021","journal-title":"Quantum Mach. Intell."},{"key":"mlstacf096bib22","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/abd891","article-title":"Large gradients via correlation in random parameterized quantum circuits","volume":"6","author":"Volkoff","year":"2021","journal-title":"Quantum Sci. Technol."},{"key":"mlstacf096bib23","doi-asserted-by":"publisher","first-page":"214","DOI":"10.22331\/q-2019-12-09-214","article-title":"An initialization strategy for addressing barren plateaus in parametrized quantum circuits","volume":"3","author":"Grant","year":"2019","journal-title":"Quantum"},{"key":"mlstacf096bib24","article-title":"Permutation invariant encodings for quantum machine learning with point cloud data","author":"Heredge","year":"2023"},{"key":"mlstacf096bib25","doi-asserted-by":"publisher","DOI":"10.1002\/qute.202300130","article-title":"Boosted ensembles of qubit and continuous variable quantum support vector machines for b meson flavour tagging","author":"West","year":"2023","journal-title":"Adv. Quantum Technol."},{"key":"mlstacf096bib26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.033212","article-title":"Quantum adversarial machine learning","volume":"2","author":"Lu","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"mlstacf096bib27","article-title":"Demystify problem-dependent power of quantum neural networks on multi-class classification","author":"Du","year":"2022"},{"key":"mlstacf096bib28","first-page":"235","article-title":"Nachrichten von der Gesellschaft der Wissenschaften zu G\u00f6ttingen, Mathematisch-Physikalische Klasse","volume":"1918","author":"Noether","year":"1918","journal-title":"Invariante Variationsprobleme"},{"key":"mlstacf096bib29","article-title":"Equivariant convolutional networks","author":"Cohen","year":"2021"},{"key":"mlstacf096bib30","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"Lecun","year":"1998","journal-title":"Proc. IEEE"},{"key":"mlstacf096bib31","first-page":"pp 2747","article-title":"On the generalization of equivariance and convolution in neural networks to the action of compact groups","author":"Kondor","year":"2018"},{"key":"mlstacf096bib32","first-page":"pp 770","article-title":"Deep residual learning for image recognition","author":"He","year":"2016"},{"key":"mlstacf096bib33","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/MSP.2017.2693418","article-title":"Geometric deep learning: going beyond Euclidean data","volume":"34","author":"Bronstein","year":"2017","journal-title":"IEEE Signal Process. Mag."},{"key":"mlstacf096bib34","article-title":"Geometric deep learning: grids, groups, graphs, geodesics, and gauges","author":"Bronstein","year":"2021"},{"key":"mlstacf096bib35","article-title":"Group-equivariant neural networks with fusion diagrams","author":"Li","year":"2022"},{"key":"mlstacf096bib36","first-page":"pp 701","article-title":"Deepwalk: online learning of social representations","author":"Perozzi","year":"2014"},{"key":"mlstacf096bib37","first-page":"pp 37","article-title":"Geodesic convolutional neural networks on riemannian manifolds","author":"Masci","year":"2015"},{"key":"mlstacf096bib38","article-title":"Exploiting symmetry in variational quantum machine learning","author":"Meyer","year":"2022"},{"key":"mlstacf096bib39","article-title":"Representation theory for geometric quantum machine learning","author":"Ragone","year":"2022"},{"key":"mlstacf096bib40","article-title":"Theory for equivariant quantum neural networks","author":"Nguyen","year":"2022"},{"key":"mlstacf096bib41","article-title":"Theoretical guarantees for permutation-equivariant quantum neural networks","author":"Schatzki","year":"2022"},{"key":"mlstacf096bib42","article-title":"Building spatial symmetries into parameterized quantum circuits for faster training","author":"Sauvage","year":"2022"},{"key":"mlstacf096bib43","article-title":"Equivariant quantum circuits for learning on weighted graphs","author":"Skolik","year":"2022"},{"key":"mlstacf096bib44","doi-asserted-by":"crossref","DOI":"10.1103\/PRXQuantum.3.030341","article-title":"Group-invariant quantum machine learning","author":"Larocca","year":"2022"},{"key":"mlstacf096bib45","article-title":"Benchmarking variational quantum circuits with permutation symmetry","author":"Zheng","year":"2022"},{"key":"mlstacf096bib46","article-title":"Covariant quantum kernels for data with group structure","author":"Glick","year":"2021"},{"key":"mlstacf096bib47","article-title":"Learning multiple layers of features from tiny images","author":"Krizhevsky","year":"2009"},{"key":"mlstacf096bib48","first-page":"pp 3676","article-title":"From facial parts responses to face detection: a deep learning approach","author":"Yang","year":"2015"},{"key":"mlstacf096bib49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.102.032420","article-title":"Robust data encodings for quantum classifiers","volume":"102","author":"LaRose","year":"2020","journal-title":"Phys. Rev. A"},{"key":"mlstacf096bib50","first-page":"pp 247","article-title":"Logic synthesis for quantum state generation","author":"Niemann","year":"2016"},{"key":"mlstacf096bib51","first-page":"pp 272","article-title":"Synthesis of quantum logic circuits","author":"Shende","year":"2005"},{"key":"mlstacf096bib52","article-title":"GASP\u2014a genetic algorithm for state preparation","author":"Creevey","year":"2023"},{"key":"mlstacf096bib53","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/aaf59e","article-title":"Machine learning method for state preparation and gate synthesis on photonic quantum computers","volume":"4","author":"Arrazola","year":"2019","journal-title":"Quantum Sci. Technol."},{"key":"mlstacf096bib54","article-title":"Pennylane: automatic differentiation of hybrid quantum-classical computations","author":"Bergholm","year":"2018"},{"key":"mlstacf096bib55","first-page":"543","article-title":"A method for solving the convex programming problem with convergence rate o(1\/k2)","volume":"269","author":"Nesterov","year":"1983","journal-title":"Proc. USSR Acad. Sci."}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T10:04:54Z","timestamp":1692871494000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/acf096"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,24]]},"references-count":55,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,8,24]]},"published-print":{"date-parts":[[2023,9,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/acf096","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,24]]},"assertion":[{"value":"Reflection equivariant quantum neural networks for enhanced image classification","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2023 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2023-07-20","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-08-15","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-08-24","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}