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Intell."],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Quantum machine learning researchers often rely on incorporating tensor networks (TN) into deep neural networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable weights of each model layer suffer from the correlations and entanglement structure between the model parameters in classical implementations. To address this issue, a multi-layer design of a tensor ring optimized variational quantum learning classifier (Quan-TR) comprising cascading entangling gates replacing the fully connected (dense) layers of a TN is proposed, and it is referred to as tensor ring optimized quantum-enhanced tensor neural networks (TR-QNet). TR-QNet parameters are optimized using the stochastic gradient descent algorithm on qubit measurements. The proposed TR-QNet is evaluated on three distinct datasets, namely Iris, MNIST, and CIFAR-10, to demonstrate the enhanced precision achieved for binary classification. In quantum simulations, the proposed TR-QNet achieves promising precision of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$94.5\\%$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mn>94.5<\/mml:mn>\n                            <mml:mo>%<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$86.16\\%$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mn>86.16<\/mml:mn>\n                            <mml:mo>%<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$83.54\\%$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mn>83.54<\/mml:mn>\n                            <mml:mo>%<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    on the Iris, MNIST, and CIFAR-10 datasets. Benchmark studies have been conducted on state-of-the-art quantum and classical implementations of TN models to show the efficacy of the proposed TR-QNet. Moreover, the scalability of TR-QNet highlights its potential for exhibiting in deep learning applications on a large scale. The PyTorch implementation of TR-QNet is available on Github\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/github.com\/konar1987\/TR-QNet\/\" ext-link-type=\"uri\">https:\/\/github.com\/konar1987\/TR-QNet\/<\/jats:ext-link>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/s42484-025-00281-5","type":"journal-article","created":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T08:24:59Z","timestamp":1745310299000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tensor ring optimized quantum-enhanced tensor neural networks"],"prefix":"10.1007","volume":"7","author":[{"given":"Debanjan","family":"Konar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dheeraj","family":"Peddireddy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bijaya K.","family":"Panigrahi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vaneet","family":"Aggarwal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,4,22]]},"reference":[{"key":"281_CR1","doi-asserted-by":"publisher","unstructured":"Abbas A, Sutter D, Zoufal C et al (2021) The power of quantum neural networks. 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