{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:52:41Z","timestamp":1773931961070,"version":"3.50.1"},"reference-count":82,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T00:00:00Z","timestamp":1656028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12175002"],"award-info":[{"award-number":["12175002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["1222020"],"award-info":[{"award-number":["1222020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["12175002"],"award-info":[{"award-number":["12175002"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["1222020"],"award-info":[{"award-number":["1222020"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NCUT Talents Project and Special Fund","award":["12175002"],"award-info":[{"award-number":["12175002"]}]},{"name":"NCUT Talents Project and Special Fund","award":["1222020"],"award-info":[{"award-number":["1222020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-\u03c6-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-\u03c6-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices.<\/jats:p>","DOI":"10.3390\/e24070867","type":"journal-article","created":{"date-parts":[[2022,6,25]],"date-time":"2022-06-25T10:39:13Z","timestamp":1656153553000},"page":"867","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Quantum Simulation of Pseudo-Hermitian-\u03c6-Symmetric Two-Level Systems"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8942-6651","authenticated-orcid":false,"given":"Chao","family":"Zheng","sequence":"first","affiliation":[{"name":"Department of Physics, College of Science, North China University of Technology, Beijing 100144, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1007\/BF01343196","article-title":"Quantum Theory at Nucleus","volume":"51","author":"Gamow","year":"1928","journal-title":"Z. 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