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
The quantum Schur and Clebsch-Gordan transforms: I. efficient qudit circuits
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Mathematical Methods in Computer Science
Quantum algorithms for Simon's problem over nonabelian groups
ACM Transactions on Algorithms (TALG)
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
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
Quantum Computation and the Evaluation of Tensor Networks
SIAM Journal on Computing
Finding conjugate stabilizer subgroups in PSL(2; q) and related groups
Quantum Information & Computation
Quantum guessing via Deutsch-Jozsa
Quantum Information & Computation
For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets
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
Quantum algorithm for the Boolean hidden shift problem
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Solutions to the hidden subgroup problem on some metacyclic groups
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
Reduction from non-injective hidden shift problem to injective hidden shift problem
Quantum Information & Computation
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present a quantum algorithm for the dihedral hidden subgroup problem (DHSP) with time and query complexity $2^{O(\sqrt{\log\ N})}$. In this problem an oracle computes a function $f$ on the dihedral group $D_N$ which is invariant under a hidden reflection in $D_N$. By contrast, the classical query complexity of DHSP is $O(\sqrt{N})$. The algorithm also applies to the hidden shift problem for an arbitrary finitely generated abelian group.The algorithm begins as usual with a quantum character transform, which in the case of $D_N$ is essentially the abelian quantum Fourier transform. This yields the name of a group representation of $D_N$, which is not by itself useful, and a state in the representation, which is a valuable but indecipherable qubit. The algorithm proceeds by repeatedly pairing two unfavorable qubits to make a new qubit in a more favorable representation of $D_N$. Once the algorithm obtains certain target representations, direct measurements reveal the hidden subgroup.