Minimum asymptotic error of algorithms for solving ODE
Journal of Complexity
On sequential and parallel solution of initial value problems
Journal of Complexity
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum complexity of integration
Journal of Complexity
Quantum summation with an application to integration
Journal of Complexity
Quantum approximation I. Embeddings of finite-dimensional Lp spaces
Journal of Complexity
Quantum approximation II. Sobolev embeddings
Journal of Complexity
Classical and Quantum Complexity of the Sturm--Liouville Eigenvalue Problem
Quantum Information Processing
On the Complexity of Searching for a Maximum of a Function on a Quantum Computer
Quantum Information Processing
Improved bounds on the randomized and quantum complexity of initial-value problems
Journal of Complexity
Complexity of initial-value problems for ordinary differential equations of order k
Journal of Complexity
Almost optimal solution of initial-value problems by randomized and quantum algorithms
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
The quantum query complexity of elliptic PDE
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
The randomized complexity of initial value problems
Journal of Complexity
Improved bounds on the randomized and quantum complexity of initial-value problems
Journal of Complexity
Numerical analysis on a quantum computer
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Hi-index | 0.00 |
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration and approximation problems, for which a speed-up is shown in many important cases by quantum computers with respect to deterministic and randomized algorithms on a classical computer. In this paper, we deal with the randomized and quantum complexity of initial-value problems. For this nonlinear problem, we show that both randomized and quantum algorithms yield a speed-up over deterministic algorithms. Upper bounds on the complexity in the randomized and quantum settings are shown by constructing algorithms with a suitable cost, where the construction is based on integral information. Lower bounds result from the respective bounds for the integration problem.