Designing programs that check their work
Journal of the ACM (JACM)
Regular Article: On Quantum Algorithms for Noncommutative Hidden Subgroups
Advances in Applied Mathematics
A nonadaptive NC checker for permutation group intersection
Theoretical Computer Science
Quantum computation and quantum information
Quantum computation and quantum information
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum Computation and Lattice Problems
SIAM Journal on Computing
The quantum query complexity of the hidden subgroup problem is polynomial
Information Processing Letters - Devoted to the rapid publication of short contributions to information processing
The hidden subgroup problem and permutation group theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The Symmetric Group Defies Strong Fourier Sampling
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Limitations of quantum coset states for graph isomorphism
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the impossibility of a quantum sieve algorithm for graph isomorphism
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Algorithms for Hidden Nonlinear Structures
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
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We show that several problems that figure prominently in quantum computing, including HIDDEN COSET, HIDDEN SHIFT, and ORBIT COSET, are equivalent or reducible to HIDDEN SUBGROUP. We also show that, over permutation groups, the decision version and search version of HIDDEN SUBGROUP are polynomial-time equivalent. For HIDDEN SUBGROUP over dihedral groups, such an equivalence can be obtained if the order of the group is smooth. Finally, we give nonadaptive program checkers for HIDDEN SUBGROUP and its decision version.