{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T19:42:29Z","timestamp":1768074149478,"version":"3.49.0"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Soft. Eng. Knowl. Eng."],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p> It is widely understood that quantum computing \u2014 quantum gates upon qubits \u2014 is the general case, encompassing computing by classical means, viz. Boolean logic upon classical bits. It also seems reasonable that Quantum Software should encompass Classical Software. However, to accept such a statement regarding software, the feeling that it seems reasonable is not enough. One needs clear-cut definitions and formal conclusions. This is exactly the purpose of this paper. Previously, we have represented Classical Software by the Laplacian Matrix. More recently, we have shown that Quantum Software is faithfully represented by Density Matrices. It turns out that a Laplacian Matrix normalized by the Laplacian Trace easily obtains a Density Matrix. This opens the horizons for Quantum Software operations \u2014 such as unitary and reversible evolution \u2014 not naturally available with the classical Laplacian. This paper provides the necessary definitions and conclusions, illustrating the more general Quantum operations with a relevant case study, playing the double role of both classical and quantum software. <\/jats:p>","DOI":"10.1142\/s0218194024410043","type":"journal-article","created":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T04:10:41Z","timestamp":1722053441000},"page":"1441-1456","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Software Encompasses Classical Software: Density Matrix from the Laplacian"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9917-3950","authenticated-orcid":false,"given":"Iaakov","family":"Exman","sequence":"first","affiliation":[{"name":"School of Computer Science, Faculty of Sciences, HIT \u2013 Holon Institute of Technology, Holon 5810201, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,9,30]]},"reference":[{"key":"S0218194024410043BIB001","volume-title":"The Essence of Software \u2013 Why Concepts Matter for Great Design","author":"Jackson D.","year":"2021"},{"key":"S0218194024410043BIB002","volume-title":"The Design of Design: Essays from a Computer Scientist","author":"Brooks F. 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