Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum algorithms for solvable groups
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Security of Signed ElGamal Encryption
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Classical and Quantum Computation
Classical and Quantum Computation
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On The Complexity Of Matrix Group Problems I
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
The quantum query complexity of the determinant
Information Processing Letters
The quantum complexity of group testing
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum property testing of group solvability
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Finding is as easy as detecting for quantum walks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The quantum query complexity of algebraic properties
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
| Hi-index | 0.00 |
We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is in Õ(k2/3). The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of Ω(k2/3), we introduce a new technique of reduction for quantum query complexity. Along the way, we prove the optimality of the algorithm of Pak for the randomized model.