By Ming Yang Kao

"The Encyclopedia of Algorithms" will supply a entire set of recommendations to big algorithmic difficulties for college students and researchers drawn to fast finding priceless details. the 1st variation of the reference will concentrate on high-impact ideas from the latest decade; later variations will widen the scope of the paintings. approximately 500 entries could be equipped alphabetically through challenge, with sub entries making an allowance for specific ideas and particular situations to be indexed by way of the 12 months. An access will comprise: an outline of the elemental algorithmic challenge; the enter and output requisites; the main effects; examples of purposes; and, citations to the most important literature. Open difficulties, hyperlinks to obtain capable code, experimental effects, information units, and illustrations can be supplied. All entries can be written through specialists; hyperlinks to websites that define their study paintings can be supplied. The entries might be peer-reviewed. This defining reference might be released in print and on-line. The print booklet will contain an index of topics and authors in addition to a chronology for finding fresh options. the net variation will complement this index with hyper hyperlinks in addition to contain hyper hyperlinks within the textual content of the entries to comparable entries, Refer citations, and different worthwhile URLs pointed out above.

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Springer, London (1998) 14. : Algorithms for Quantum Computation: Discrete Logarithms and Factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134, Santa Fe, 20–22 November 1994 15. : Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM J. Comp. 26, 1484–1509 (1997) 16. : On the power of quantum computation. In: Proceedings of the 35th IEEE Symposium on the Foundations of Computer Science (FOCS), pp.

Theorem (Abelian hidden subgroup problem) There exists a quantum algorithm that, given an instance of the Abelian hidden subgroup problem, makes n + O(1) queries to U f , uses poly(n) other elementary quantum and classical operations, and with probability at least 2/3 outputs values h1 ; h2 ; : : : ; h l such that K = hh1 i ˚ hh2 i ˚ hh l i. In some cases, the success probability can be made 1 with the same complexity, and in general the success probability can be made 1 using n + O(log(1/ )) queries and Abelian Hidden Subgroup Problem pol y(n; log(1/ )) other elementary quantum and classical operations.

424– 437, Santa Barbara, 27–31 August 1995 2. : An exact quantum polynomial-time algorithm for Simon’s problem. In: Proc. of Fifth Israeli Symposium on Theory of Computing ans Systems (ISTCS’97), pp. 12– 23 (1997) and in: Proceedings IEEE Computer Society, RamatGan, 17–19 June 1997 3. : Decomposing Finite Abelian Groups. Quantum Inf. Comp. 1(2), 26–32 (2001) 4. : Quantum Algorithms Revisited. Proc. Royal Soc. London A 454, 339–354 (1998) 5. : Quantum theory, the Church-Turing principle and the universal quantum computer.