Eigenvalues and s-numbers
Information-based complexity
A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth 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
An Introduction to Quantum Computing Algorithms
An Introduction to Quantum Computing Algorithms
Quantum computation and quantum information
Quantum computation and quantum information
Quantum summation with an application to integration
Journal of Complexity
On a problem in quantum summation
Journal of Complexity
Quantum integration in Sobolev classes
Journal of Complexity
Path Integration on a Quantum Computer
Quantum Information Processing
From Monte Carlo to quantum computation
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Quantum approximation II. Sobolev embeddings
Journal of Complexity
Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers
Foundations of Computational Mathematics
Sharp error bounds on quantum Boolean summation in various settings
Journal of Complexity
Quantum approximation II. Sobolev embeddings
Journal of Complexity
Randomized and quantum algorithms yield a speed-up for initial-value problems
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
The randomized information complexity of elliptic PDE
Journal of Complexity
Improved bounds on the randomized and quantum complexity of initial-value problems
Journal of Complexity
The Quantum Setting with Randomized Queries for Continuous Problems
Quantum Information Processing
A lower bound for the Sturm-Liouville eigenvalue problem on a quantum computer
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 Sturm-Liouville Eigenvalue Problem and NP-Complete Problems in the Quantum Setting with Queries
Quantum Information Processing
Quantum lower bounds by entropy numbers
Journal of Complexity
Improved bounds on the randomized and quantum complexity of initial-value problems
Journal of Complexity
The randomized information complexity of elliptic PDE
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 |
We study approximation of embeddings between finite-dimensional Lp spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The results show that for certain regions of the parameter domain quantum computation can essentially improve the rate of convergence of classical deterministic or randomized approximation, while there are other regions where the best possible rates coincide for all three settings. These results serve as a crucial building block for analyzing approximation in function spaces in a subsequent paper (Quantum approximation II. Sobolev Embeddings, J. Complexity, submitted).