STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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 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
Quantum mechanical algorithms for the nonabelian hidden subgroup problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Computation and Lattice Problems
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
An improved quantum Fourier transform algorithm and applications
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Generic quantum Fourier transforms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The power of basis selection in fourier sampling: hidden subgroup problems in affine groups
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
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 algorithms for Simon's problem over general groups
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithms for Simon's problem over nonabelian groups
ACM Transactions on Algorithms (TALG)
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
On the complexity of the hidden subgroup problem
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Finding conjugate stabilizer subgroups in PSL(2; q) and related groups
Quantum Information & Computation
For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets
Quantum Information & Computation
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
Quantum algorithms for shifted subset problems
Quantum Information & Computation
On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
Quantum Information & Computation
Efficient quantum algorithms for the hidden subgroup problem over semi-direct product groups
Quantum Information & Computation
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We resolve the question of whether Fourier sampling can efficiently solve the hidden subgroup problem in general groups. Specifically, we show that the hidden subgroup problem in the symmetric group cannot be efficiently solved by strong Fourier sampling. Indeed we prove the stronger statement that no measurement of a single coset state can reveal more than an exponentially small amount of information about the identity of the hidden subgroup, in the special case relevant to the Graph Isomorphism problem.