Testing shift-equivalence of polynomials by deterministic, probabilistic and quantum machines
Theoretical Computer Science
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
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Complexity theory retrospective II
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Quantum Fourier sampling simplified
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Quantum algorithms for solvable groups
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The hidden subgroup problem and permutation group theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum solution to the hidden subgroup problem for poly-near-hamiltonian groups
Quantum Information & Computation
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Quantum algorithms for factoring and finding discrete logarithms have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. We present a quantum algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear number of calls to the input function. We also explore the difficulties of developing an algorithm to process the data to explicitly calculate a generating set for the subgroup. A general framework for the noncommutative hidden subgroup problem is discussed and we indicate future research directions.