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Asymptotically fast triangularization of matrices over rings
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Bounded round interactive proofs in finite groups
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A course in computational algebraic number theory
A course in computational algebraic number theory
Fast Monte Carlo algorithms for permutation groups
Selected papers of the 23rd annual ACM symposium on Theory of computing
Testing shift-equivalence of polynomials using quantum machines
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Solvable black-box group problems are low for PP
Theoretical Computer Science
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
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Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Succinct quantum proofs for properties of finite groups
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
On quantum algorithms for noncommutative hidden subgroups
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Hidden translation and orbit coset in quantum computing
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Adiabatic quantum state generation and statistical zero knowledge
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Exponential algorithmic speedup by a quantum walk
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Generic quantum Fourier transforms
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FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A polynomial quantum algorithm for approximating the Jones polynomial
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Quantum computation of zeta functions of curves
Computational Complexity
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Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
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Quantum property testing of group solvability
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Quantum Computation and the Evaluation of Tensor Networks
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Quantum Information & Computation
Quantum solution to the hidden subgroup problem for poly-near-hamiltonian groups
Quantum Information & Computation
Efficient quantum algorithms for the hidden subgroup problem over semi-direct product groups
Quantum Information & Computation
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Quantum algorithms for a set of group theoretic problems
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Quantum complexity of testing group commutativity
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Finding hidden Borel subgroups of the general linear group
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Exponential quantum speed-ups are generic
Quantum Information & Computation
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In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a subgroup in a given solvable group, reduce to computing orders of solvable groups and therefore admit polynomial-time quantum algorithms as well. Our algorithm works in the setting of black-box groups, wherein none of these problems have polynomial-time classical algorithms. As an important byproduct, our algorithm is able to produce a pure quantum state that is uniform over the elements in any chosen subgroup of a solvable group, which yields a natural way to apply existing quantum algorithms to factor groups of solvable groups.