ar X iv : q ua nt - p h / 02 11 09 1 v 1 1 5 N ov 2 00 2 Hidden Translation and Orbit Coset in Quantum Computing ∗
نویسندگان
چکیده
We give efficient quantum algorithms for HIDDEN TRANSLATION and HIDDEN SUBGROUP in a large class of non-abelian groups including solvable groups of bounded exponent and of bounded derived series. Our algorithms are recursive. For the base case, we solve efficiently HIDDEN TRANSLATION in Z p , whenever p is a fixed prime. For the induction step, we introduce the problem ORBIT COSET generalizing both HIDDEN TRANSLATION and HIDDEN SUBGROUP, and prove a powerful selfreducibility result: ORBIT COSET in a finite group G, is reducible to ORBIT COSET in G/N and subgroups of N , for any solvable normal subgroupN of G.
منابع مشابه
ar X iv : q ua nt - p h / 02 11 09 1 v 4 1 6 Se p 20 13 Hidden Translation and Translating Coset in Quantum Computing ∗
We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Zp , whenever p is a fixed prime. For the induction step, we introduce the ...
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