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Due to the complex potential, the evolution mixes real- and imaginary-time propagation and the wave function can potentially be continuously absorbed during the time propagation. We use the dilation quantum algorithm to treat the imaginary-time evolution in parallel to the real-time propagation. This method has the advantage of using only one reservoir qubit at a time, that is measured with a certain success probability to implement the desired imaginary-time evolution. We propose a specific prescription for the dilation method where the success probability is directly linked to the physical norm of the continuously absorbed state evolving on the mesh. We expect that the proposed prescription will have the advantage of keeping a high probability of success in most physical situations. Applications of the method are made on one-dimensional wave functions evolving on a mesh. Results obtained on a quantum computer identify with those obtained on a classical computer. We finally give a detailed discussion on the complexity of implementing the dilation matrix. Due to the local nature of the potential, for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>n<\/mml:mi><\/mml:math> qubits, the dilation matrix only requires <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>2<\/mml:mn><mml:mi>n<\/mml:mi><\/mml:msup><\/mml:math> CNOT and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>2<\/mml:mn><mml:mi>n<\/mml:mi><\/mml:msup><\/mml:math> unitary rotation for each time step, whereas it would require of the order of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>4<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math> C-NOT gates to implement it using the best-known algorithm for general unitary matrices.<\/jats:p>","DOI":"10.22331\/q-2024-04-08-1311","type":"journal-article","created":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T16:26:01Z","timestamp":1712593561000},"page":"1311","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Efficient solution of the non-unitary time-dependent Schrodinger equation on a quantum computer with complex absorbing potential"],"prefix":"10.22331","volume":"8","author":[{"given":"Mariane","family":"Mangin-Brinet","sequence":"first","affiliation":[{"name":"Laboratoire de Physique Subatomique et de Cosmologie, CNRS\/IN2P3, 38026 Grenoble, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Zhang","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS\/IN2P3, IJCLab, 91405 Orsay, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denis","family":"Lacroix","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS\/IN2P3, IJCLab, 91405 Orsay, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edgar Andres","family":"Ruiz Guzman","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS\/IN2P3, IJCLab, 91405 Orsay, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2024,4,8]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. 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