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Robust Quantum Algorithms Computing OR with ε-Biased Oracles Tomoya SUZUKI Shigeru YAMASHITA Masaki NAKANISHI Katsumasa WATANABE Publication IEICE TRANSACTIONS on Information and Systems Vol.E90-D No.2 pp.395-402 Publication Date: 2007/02/01 Online ISSN: 1745-1361 DOI: 10.1093/ietisy/e90-d.2.395 Print ISSN: 0916-8532 Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science) Category: Quantum Computing Keyword: quantum computing, biased oracle, phase estimation, Full Text: PDF(245.7KB)>>
Summary: This paper considers the quantum query complexity of ε-biased oracles that return the correct value with probability only 1/2 + ε. In particular, we show a quantum algorithm to compute N-bit OR functions with O(  /ε) queries to ε-biased oracles. This improves the known upper bound of O(/ε2) and matches the known lower bound; we answer the conjecture raised by the paper [1] affirmatively. We also show a quantum algorithm to cope with the situation in which we have no knowledge about the value of ε. This contrasts with the corresponding classical situation, where it is almost hopeless to construct a bounded error algorithm without knowing the value of ε. | ||||||||||
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