Theory of linear and integer programming
Theory of linear and integer programming
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
Quantum algorithms for solvable groups
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
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
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
An algorithm for computing a basis of a finite abelian group
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Property testing for cyclic groups and beyond
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Linear time algorithms for the basis of abelian groups
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Finding hidden Borel subgroups of the general linear group
Quantum Information & Computation
Property testing for cyclic groups and beyond
Journal of Combinatorial Optimization
On the probability of generating a lattice
Journal of Symbolic Computation
Classical simulations of Abelian-group normalizer circuits with intermediate measurements
Quantum Information & Computation
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This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups into a product of cyclic groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to be at least as difficult as factoring).