A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth 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
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Stabilization of Quantum Computations by Symmetrization
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
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
STOC '02 Proceedings of the thiry-fourth 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 Hash and Claw-Free Functions
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
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
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
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Fast quantum algorithms for computing the unit group and class group of a number field
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Polynomial time quantum algorithm for the computation of the unit group of a number field
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
SIAM Journal on Computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
Applications of coherent classical communication and the schur transform to quantum information theory
The quantum Schur and Clebsch-Gordan transforms: I. efficient qudit circuits
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum solution to the hidden subgroup problem for poly-near-hamiltonian groups
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
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
Quantum Information & Computation
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Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem.We observe that simply measuring the partition (a procedure we call weak Schur sampling) provides very little information about the hidden subgroup. Furthermore, we show that under quite general assumptions, even a combination of weak Fourier sampling and weak Schur sampling fails to identify the hidden subgroup. We also prove tight bounds on how many coset states are required to solve the hidden subgroup problem by weak Schur sampling, and we relate this question to a quantum version of the collision problem.