Fast Monte Carlo algorithms for permutation groups
Selected papers of the 23rd 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
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
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
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 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 quantum information
Quantum computation and quantum information
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Classical and Quantum Computation
Classical and Quantum Computation
Decomposing finite Abelian groups
Quantum Information & Computation
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
The hidden subgroup problem and permutation group theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
Journal of the ACM (JACM)
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
Adversary Lower Bounds for Nonadaptive Quantum Algorithms
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Mathematical Methods in Computer Science
Quantum Testers for Hidden Group Properties
Fundamenta Informaticae - Machines, Computations and Universality, Part II
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
On the complexity of the hidden subgroup problem
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
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
Adversary lower bounds for nonadaptive quantum algorithms
Journal of Computer and System Sciences
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
Complexity classes of equivalence problems revisited
Information and Computation
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
Quantum solution to the hidden subgroup problem for poly-near-hamiltonian groups
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
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
New algorithms for learning in presence of errors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Quantum algorithm for the Boolean hidden shift problem
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Quantum algorithms for a set of group theoretic problems
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
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
Finding hidden Borel subgroups of the general linear group
Quantum Information & Computation
Quantum Testers for Hidden Group Properties
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Reduction from non-injective hidden shift problem to injective hidden shift problem
Quantum Information & Computation
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
| Hi-index | 0.00 |
We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Z pn, whenever p is a fixed prime. For the induction step, we introduce the problem Orbit Coset generalizing both Hidden Translation and Hidden Subgroup, and prove a powerful self-reducibility result: Orbit Coset in a finite group G is reducible to Orbit Coset in G/N and subgroups of N, for any solvable normal subgroup N of G.