Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum algorithms for solvable groups
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum mechanical algorithms for the nonabelian hidden subgroup problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On quantum algorithms for noncommutative hidden subgroups
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Quantum measurements for hidden subgroup problems with optimal sample complexity
Quantum Information & Computation
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
Quantum Information & Computation
On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
Quantum Information & Computation
On the power of random bases in fourier sampling: hidden subgroup problem in the heisenberg group
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Finding hidden Borel subgroups of the general linear group
Quantum Information & Computation
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The Hidden Subgroup Problem (HSP) has been widely studied in the context of quantum computing and is known to be efficiently solvable for Abelian groups, yet appears to be difficult for many non-Abelian ones. An efficient algorithm for the HSP over a group G runs in time polynomial in n def = log|G|. For any subgroup H of G, let N(H) denote the normalizer of H. Let MG denote the intersection of all normalizers in G (i.e., MG = ∩H≤GN(H)). MG is always a subgroup of G and tile index [G:MG] can be taken as a measure of "how non-Abelian" G is ([G : MG] = 1 for Abelian groups). This measure was considered by Grigni, Sehulman. Vazirani and Vazirani. who showed that whenever [G : MG] ∈ exp(O(log1/2 n)) the corresponding HSP can be solved efficiently (under certain assumptions). We show that whenever [G : MG] ∈ poly(n) the corresponding HSP can be solved efficiently, under the same assumptions (actually, we solve a slightly more general case of the HSP and also show that some assnmptions may be relaxed).