Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
A course in computational algebraic number theory
A course in computational algebraic number theory
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Regular Article: On Quantum Algorithms for Noncommutative Hidden Subgroups
Advances in Applied Mathematics
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
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
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
Quantum solution to the hidden subgroup problem for poly-near-hamiltonian groups
Quantum Information & Computation
On the complexity of the hidden subgroup problem
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Quantum algorithms for highly non-linear Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
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
Quantum algorithm for the Boolean hidden shift problem
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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Consider the following generalized hidden shift problem: given a function f on {0,..., M - 1} x ZN promised to be injective for fixed b and satisfying f(b, x) = f(b + 1,x + s) for b = 0, 1,..., M - 2, find the unknown shift s ε ZN. For M = N, this problem is an instance of the abelian hidden subgroup problem, which can be solved efficiently on a quantum computer, whereas for M = 2, it is equivalent to the dihedral hidden subgroup problem, for which no efficient algorithm is known. For any fixed positive ε, we give an efficient (i.e., poly(log N)) quantum algorithm for this problem provided M ≥ Nε. The algorithm is based on the "pretty good measurement" and uses H. Lenstra's (classical) algorithm for integer programming as a subroutine.