{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T04:12:13Z","timestamp":1775880733080,"version":"3.50.1"},"publisher-location":"Cham","reference-count":49,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783031131875","type":"print"},{"value":"9783031131882","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,8,6]],"date-time":"2022-08-06T00:00:00Z","timestamp":1659744000000},"content-version":"vor","delay-in-days":217,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Due to the beyond-classical capability of quantum computing, quantum machine learning is applied independently or embedded in classical models for decision making, especially in the field of finance. Fairness and other ethical issues are often one of the main concerns in decision making. In this work, we define a formal framework for the fairness verification and analysis of quantum machine learning decision models, where we adopt one of the most popular notions of fairness in the literature based on the intuition\u2014any two similar individuals must be treated similarly and are thus unbiased. We show that quantum noise can improve fairness and develop an algorithm to check whether a (noisy) quantum machine learning model is fair. In particular, this algorithm can find bias kernels of quantum data (encoding individuals) during checking. These bias kernels generate infinitely many bias pairs for investigating the unfairness of the model. Our algorithm is designed based on a highly efficient data structure\u2014Tensor Networks\u2014and implemented on Google\u2019s TensorFlow Quantum. The utility and effectiveness of our algorithm are confirmed by the experimental results, including income prediction and credit scoring on real-world data, for a class of random (noisy) quantum decision models with 27 qubits (<jats:inline-formula><jats:alternatives><jats:tex-math>$$2^{27}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>2<\/mml:mn><mml:mn>27<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-dimensional state space) tripling (<jats:inline-formula><jats:alternatives><jats:tex-math>$$2^{18}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>2<\/mml:mn><mml:mn>18<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>times more than) that of the state-of-the-art algorithms for verifying quantum machine learning models.<\/jats:p>","DOI":"10.1007\/978-3-031-13188-2_20","type":"book-chapter","created":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T08:16:57Z","timestamp":1659687417000},"page":"408-429","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Verifying Fairness in\u00a0Quantum Machine Learning"],"prefix":"10.1007","author":[{"given":"Ji","family":"Guan","sequence":"first","affiliation":[]},{"given":"Wang","family":"Fang","sequence":"additional","affiliation":[]},{"given":"Mingsheng","family":"Ying","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,6]]},"reference":[{"key":"20_CR1","doi-asserted-by":"crossref","unstructured":"Arute, F., et\u00a0al.: Quantum supremacy using a programmable superconducting processor. 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