Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth 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
Regular Article: On Quantum Algorithms for Noncommutative Hidden Subgroups
Advances in Applied Mathematics
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
Quantum Computation and Lattice Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
The Symmetric Group Defies Strong Fourier Sampling
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Quantum solution to the hidden subgroup problem for poly-near-hamiltonian groups
Quantum Information & Computation
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
Classical and Quantum Algorithms for Exponential Congruences
Theory of Quantum Computation, Communication, and Cryptography
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Mathematical Methods in Computer Science
Quantum algorithms using the curvelet transform
Proceedings of the forty-first annual ACM symposium on Theory of computing
Quantum algorithms for Simon's problem over nonabelian groups
ACM Transactions on Algorithms (TALG)
An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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
An efficient quantum algorithm for the hidden subgroup problem in nil-2 groups
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Quantum algorithms for highly non-linear Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the Impossibility of a Quantum Sieve Algorithm for Graph Isomorphism
SIAM Journal on Computing
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
Efficient quantum algorithm for identifying hidden polynomials
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
On solving systems of random linear disequations
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
Solutions to the hidden subgroup problem on some metacyclic groups
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
Finding hidden Borel subgroups of the general linear group
Quantum Information & Computation
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We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem. By solving this problem, we find efficient quantum algorithms for a number of nonabelian hidden subgroup problems, including some for which no efficient algorithm was previously known: certain metacyclic groups as well as all groups of the form Z^r _p xZp for fixed r (including the Heisenberg group, r = 2). In particular, our results show that entangled measurements across multiple copies of hidden subgroup states can be useful for efficiently solving the nonabelian HSP.