{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10695","name":"Power of Uninitialized Qubits in Shallow Quantum Circuits","abstract":"We study the computational power of shallow quantum circuits\r\nwith O(log n) initialized and n^{O(1)} uninitialized ancillary\r\nqubits, where n is the input length and the initial state of\r\nthe uninitialized ancillary qubits is arbitrary. First, we show\r\nthat such a circuit can compute any symmetric function on n bits\r\nthat is classically computable in polynomial time. Then, we\r\nregard such a circuit as an oracle and show that a\r\npolynomial-time classical algorithm with the oracle can estimate\r\nthe elements of any unitary matrix corresponding to a\r\nconstant-depth quantum circuit on n qubits. Since it seems unlikely\r\nthat these tasks can be done with only O(log n) initialized\r\nancillary qubits, our results give evidences that adding\r\nuninitialized ancillary qubits increases the computational power\r\nof shallow quantum circuits with only O(log n) initialized\r\nancillary qubits. Lastly, to understand the limitations of\r\nuninitialized ancillary qubits, we focus on\r\nnear-logarithmic-depth quantum circuits with them and show\r\nthe impossibility of computing the parity function on n bits.","keywords":["quantum circuit complexity","shallow quantum circuit","uninitialized qubit"],"author":[{"@type":"Person","name":"Takahashi, Yasuhiro","givenName":"Yasuhiro","familyName":"Takahashi"},{"@type":"Person","name":"Tani, Seiichiro","givenName":"Seiichiro","familyName":"Tani"}],"position":57,"pageStart":"57:1","pageEnd":"57:13","dateCreated":"2018-02-27","datePublished":"2018-02-27","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Takahashi, Yasuhiro","givenName":"Yasuhiro","familyName":"Takahashi"},{"@type":"Person","name":"Tani, Seiichiro","givenName":"Seiichiro","familyName":"Tani"}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2018.57","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6299","volumeNumber":96,"name":"35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)","dateCreated":"2018-02-27","datePublished":"2018-02-27","editor":[{"@type":"Person","name":"Niedermeier, Rolf","givenName":"Rolf","familyName":"Niedermeier"},{"@type":"Person","name":"Vall\u00e9e, Brigitte","givenName":"Brigitte","familyName":"Vall\u00e9e"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10695","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6299"}}}