November 30, 2025 Dataset Open Access

Sergio Bengoechea; Paul Over; Thomas Rung

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{"conceptdoi":"10.25592/uhhfdm.18048","conceptrecid":"18048","created":"2025-11-04T17:02:11.647142+00:00","doi":"10.25592/uhhfdm.18049","id":18049,"links":{"badge":"https://www.fdr.uni-hamburg.de/badge/doi/10.25592/uhhfdm.18049.svg","conceptbadge":"https://www.fdr.uni-hamburg.de/badge/doi/10.25592/uhhfdm.18048.svg","conceptdoi":"http://doi.org/10.25592/uhhfdm.18048","doi":"http://doi.org/10.25592/uhhfdm.18049"},"metadata":{"access_right":"open","access_right_category":"success","communities":[{"id":"qcfd"},{"id":"uhh"}],"creators":[{"affiliation":"Institute for Fluid Dynamics and Ship Theory,  Hamburg University of Technology","name":"Sergio Bengoechea","orcid":"0009-0001-8205-5878"},{"affiliation":"Institute for Fluid Dynamics and Ship Theory,  Hamburg University of Technology","name":"Paul Over","orcid":"0000-0001-7436-5254"},{"affiliation":"Institute for Fluid Dynamics and Ship Theory,  Hamburg University of Technology","name":"Thomas Rung","orcid":"0000-0002-3454-1804"}],"description":"<p>This data belongs to the article, which presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The method adapts the linear combination of unitaries algorithm to block encode the diffusive dynamics, while arbitrary boundary conditions are enforced by the method of images only at the cost of one additional qubit per spatial dimension. As an alternative to the non-periodic reflection, the direct encoding of Neumann conditions by the unitary decomposition of the discrete time-marching operator is proposed. All presented algorithms indicate optimal success probabilities while maintaining linear time complexity, thereby securing the practical applicability of the quantum algorithm on fault-tolerant quantum computers. The proposed time-marching method is demonstrated through state-vector simulations of the heat equation in combination with Neumann, Dirichlet, and mixed boundary conditions.&nbsp;This research data is available via this repository.</p>","doi":"10.25592/uhhfdm.18049","keywords":["Quantum Time Marching","Boundary Conditions","Block Encoding","Success Probabilities"],"language":"eng","license":{"id":"CC-BY-4.0"},"notes":"The current work has received funding from the European Union's Horizon Europe research and innovation program (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10) under grant agreement No. 101080085 QCFD and by the Engineering and Physical Sciences Research Council under Grant No. EP/W032643/1.","publication_date":"2025-11-30","related_identifiers":[{"identifier":"10.25592/uhhfdm.18048","relation":"isVersionOf","scheme":"doi"}],"relations":{"version":[{"count":1,"index":0,"is_last":true,"last_child":{"pid_type":"recid","pid_value":"18049"},"parent":{"pid_type":"recid","pid_value":"18048"}}]},"resource_type":{"title":"Dataset","type":"dataset"},"title":"Quantum time-marching algorithms for solving linear transport problems including boundary conditions","version":"v1"},"owners":[569],"revision":4,"updated":"2025-11-06T11:11:31.128645+00:00"}