## 33 Citations

### On the quantum complexity of computing the median of continuous distribution

- MathematicsQuantum Inf. Comput.
- 2019

It is shown that the ε-complexity up to a logarithmic factor is of order ε−1/(r+ρ+1).

### On the Power of Quantum Algorithms for Vector Valued Mean Computation

- Mathematics, Computer ScienceMonte Carlo Methods Appl.
- 2004

It turns out that in contrast to the known superiority of quantum algorithms in the scalar case, in high dimensional L M P spaces classical randomized algorithms are essentially as powerful as quantum algorithms.

### On the quantum complexity of approximating median of continuous distribution

- Mathematics, Computer Science
- 2018

The approximating of the median of absolutely continuous distribution given by a probability density function $f$ is considered and it is shown that the $\epsilon$-complexity up to logarithmic factor is of order $Epsilon^{-1/((r+\rho+1))}$.

### Randomized and quantum complexity of nonlinear two-point BVPs

- Computer Science, MathematicsAppl. Math. Comput.
- 2014

### Complexity of solving nonlinear equations in the deterministic, randomized and quantum settings

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2013

### Sobolev Approximation in the Quantum Computation Model

- Computer Science2011 Fourth International Conference on Intelligent Computation Technology and Automation
- 2011

Using a new and elegant reduction approach we derive a lower bound of quantum complexity for the approximation of imbeddings from anisotropic Sobolev classes B(Wrp([0,1]d)) to anisotropic Sobolev…

### Quantum complexity of the approximation for the classes B(Wrp ([0, 1]d)) and B(Hrp ([0, 1]d))

- Computer Science
- 2010

### On the complexity of a two-point boundary value problem in different settings

- Computer Science, MathematicsInt. J. Comput. Math.
- 2010

This work studies the complexity of a two-point boundary value problem, and shows that the use of linear information gives us a speed-up of at least one order of magnitude compared with the standard information.

### Convergence rate of quantum algorithm for multivariate approximation

- Computer Science2010 Sixth International Conference on Natural Computation
- 2010

It turns out that for the Sobolev class B B(W<inf>p</inf><sup>r</Sup> ([0, 1]<sup>d</sup>)) (r ∈ ℕ<sup*d</ Sup>), when p < q, the quantum algorithms can bring speedup over classical deterministic and randomized algorithms.

## References

SHOWING 1-10 OF 24 REFERENCES

### Quantum Summation with an Application to Integration

- Computer ScienceJ. Complex.
- 2002

Developing quantum algorithms for computing the mean of sequences that satisfy a p-summability condition and for integration of functions from Lebesgue spaces Lp(0, 1]d, and proving lower bounds showing that the proposed algorithms are, in many cases, optimal within the setting of quantum computing.

### Information-Based Complexity

- Computer Science
- 1988

This book provides a comprehensive treatment of information-based complexity, the branch of computational complexity that deals with the intrinsic difficulty of the approximate solution of problems…

### Optimal Summation and Integration by Deterministic, Randomized, and Quantum Algorithms

- Mathematics
- 2002

We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Holder or Sobolev spaces. First we discuss optimal deterministic and…

### An Introduction to Quantum Computing Algorithms

- Computer Science
- 2000

This monograph is a good self-contained introductory resource for newcomers to the field of quantum computing algorithms, as well as a useful self-study guide for the more specialized scientist, mathematician, graduate student, or engineer.

### ON CONVERGENCE OF STOCHASTIC PROCESSES

- Mathematics
- 1962

It is clear that for given I,un } and t, the better theorem of this kind would be the one in which (2) is proved for the larger class of functions f. In this paper we shall show that certain known…