{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T09:15:31Z","timestamp":1719566131532},"reference-count":0,"publisher":"Rinton Press","issue":"9&10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2010,9]]},"abstract":"We first show how to construct an $O(n)$-depth $O(n)$-size quantum circuit for addition of two $n$-bit binary numbers with no ancillary qubits. The exact size is $7n-6$, which is smaller than that of any other quantum circuit ever constructed for addition with no ancillary qubits. Using the circuit, we then propose a method for constructing an $O(d(n))$-depth $O(n)$-size quantum circuit for addition with $O(n\/d(n))$ ancillary qubits for any $d(n) = \\Omega(\\log n)$. If we are allowed to use unbounded fan-out gates with length $O(n^{\\varepsilon})$ for an arbitrary small positive constant $\\varepsilon$, we can modify the method and construct an $O(e(n))$-depth $O(n)$-size circuit with $o(n)$ ancillary qubits for any $e(n) = \\Omega(\\log^* n)$. In particular, these methods yield efficient circuits with depth $O(\\log n)$ and with depth $O(\\log^* n)$, respectively. We apply our circuits to constructing efficient quantum circuits for Shor's discrete logarithm algorithm.<\/jats:p>","DOI":"10.26421\/qic10.9-10-12","type":"journal-article","created":{"date-parts":[[2021,3,6]],"date-time":"2021-03-06T01:25:28Z","timestamp":1614993928000},"page":"872-890","source":"Crossref","is-referenced-by-count":19,"title":["Quantum addition circuits and unbounded fan-out"],"prefix":"10.26421","volume":"10","author":[{"given":"Yasuhiro","family":"Takahashi","sequence":"first","affiliation":[]},{"given":"Seiichiro","family":"Tani","sequence":"additional","affiliation":[]},{"given":"Noboru","family":"Kunihiro","sequence":"additional","affiliation":[]}],"member":"10955","published-online":{"date-parts":[[2010,9]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,3,6]],"date-time":"2021-03-06T01:26:15Z","timestamp":1614993975000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC10.9-10-12.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":0,"journal-issue":{"issue":"9&10","published-online":{"date-parts":[[2010,9]]},"published-print":{"date-parts":[[2010,9]]}},"URL":"https:\/\/doi.org\/10.26421\/qic10.9-10-12","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"value":"1533-7146","type":"print"},{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}