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In this work, we introduce a qubit-efficient quantum circuit for integer squaring that achieves a linear qubit cost of only 3\n                    <jats:italic>N<\/jats:italic>\n                    qubits for an\n                    <jats:italic>N<\/jats:italic>\n                    -bit input, significantly outperforming state-of-the-art designs that scale quadratically in terms of qubits. Our approach reintegrates the input operand after computation, enabling the uncomputation of intermediate results and efficient recycling of ancilla qubits. This reversible strategy prevents the retention of redundant information, which is a common limitation of prior works. The comparative analysis confirms the scalability and practicality of our design for qubit-constrained quantum hardware, offering a promising solution for arithmetic operations in resource-limited quantum environments.\n                  <\/jats:p>","DOI":"10.1007\/s11227-026-08255-5","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:58:44Z","timestamp":1770983924000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Low-qubit quantum circuits for efficient integer squaring"],"prefix":"10.1007","volume":"82","author":[{"given":"Laura M.","family":"Donaire","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gloria","family":"Ortega","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ester M.","family":"Garz\u00f3n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ernestas","family":"Filatovas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco","family":"Orts","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"8255_CR1","doi-asserted-by":"crossref","unstructured":"Nielsen MA, Chuang I (2002) Quantum computation and quantum information. 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