Faster isomorphism testing of strongly regular graphs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second 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
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum Computation and Lattice Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth 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
Fast quantum algorithms for computing the unit group and class group of a number field
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
A polynomial quantum algorithm for approximating the Jones polynomial
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Limitations of quantum coset states for graph isomorphism
Proceedings of the thirty-eighth 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 algorithms using the curvelet transform
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Finding conjugate stabilizer subgroups in PSL(2; q) and related groups
Quantum Information & Computation
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
Quantum Information & Computation
Quantum fourier transform over symmetric groups
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Hi-index | 0.00 |
It is known that any quantum algorithm for Graph Isomorphism thatworks within the framework of the hidden subgroup problem (HSP) must performhighly entangled measurements across Ω(n log n) coset states. One ofthe only known models for how such a measurement could be carried outefficiently is Kuperberg's algorithm for the HSP in the dihedral group, in whichquantum states are adaptively combined and measured according to thedecomposition of tensor products into irreducible representations. This "quantum sieve" starts with coset states, and works its way down towardsrepresentations whose probabilities differ depending on, for example, whetherthe hidden subgroup is trivial or nontrivial. In this paper we show that no such approach can produce a polynomial-time quantum algorithm for Graph Isomorphism. Specifically, we consider the natural reduction of Graph Isomorphism to the HSP over the the wreath product Sn ࣀ Z2. Using a recently proved bound on the irreducible characters of Sn, we show that no algorithm in this family can solve Graph Isomorphism in less than eΩ(√n) time, no matter what adaptive rule it uses to select and combine quantum states. In particular, algorithms of this type can offer essentially no improvement over the best known classical algorithms, which run in time eO(√(n log n)).