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One of the main quantum approaches involves utilizing Hamiltonian simulation, which is directly applicable only to Schr\u00f6dinger-type equations. To address this limitation, Schr\u00f6dingerisation techniques have been developed, employing the warped transformation to convert general linear PDEs into Schr\u00f6dinger-type equations. However, despite the development of Schr\u00f6dingerisation techniques, the explicit implementation of the corresponding quantum circuit for solving general PDEs remains to be designed. In this paper, we present detailed implementation of a quantum algorithm for general PDEs using Schr\u00f6dingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme, to demonstrate the effectiveness of our approach. Complexity analysis is also carried out to demonstrate the quantum advantages of these algorithms in high dimensions over their classical counterparts.<\/jats:p>","DOI":"10.22331\/q-2024-12-12-1563","type":"journal-article","created":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T13:05:52Z","timestamp":1734008752000},"page":"1563","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":24,"title":["Quantum Circuits for partial differential equations via Schr\u00f6dingerisation"],"prefix":"10.22331","volume":"8","author":[{"given":"Junpeng","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shi","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China"},{"name":"Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China"},{"name":"MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nana","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China"},{"name":"University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai, 200240, China"},{"name":"MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China"},{"name":"Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China"},{"name":"MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Richard P Feynman. ``Simulating physics with computers''. 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