Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SIAM Journal on Computing
SIAM Journal on 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
Learning DNF over the Uniform Distribution Using a Quantum Example Oracle
SIAM Journal on Computing
Quantum Factoring, Discrete Logarithms, and the Hidden Subgroup Problem
Computing in Science and Engineering
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)
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
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
Quantum Algorithms for Hidden Nonlinear Structures
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
How Many Copies are Needed for State Discrimination?
IEEE Transactions on Information Theory
Quantum algorithms for highly non-linear Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
| Hi-index | 0.00 |
We consider a recently proposed generalisation of the abelian hidden subgroup problem:the shifted subset problem. The problem is to determine a subset S of some abeliangroup, given access to quantum states of the form |S + x〉, for some unknown shift x.We give quantum algorithms to find Hamming spheres and other subsets of the booleancube {0, 1}n. The algorithms have time complexity polynomial in n and give rise toexponential separations from classical computation.