## 36 Citations

### Optimal query error of quantum approximation on some Sobolev classes

- Computer Science, Mathematics
- 2008

The results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.

### Quantum approximation I. Embeddings of finite-dimensional Lp spaces

- Mathematics, Computer ScienceJ. Complex.
- 2004

### 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…

### Complexity for the approximation of Sobolev imbeddings in the quantum computation model

- Computer ScienceProceedings of the 30th Chinese Control Conference
- 2011

A new and elegant reduction approach is derived that quantum algorithms bring speed-up over the classical deterministic and randomized ones and this conjecture was confirmed in the situation s = 0.

### On the quantum and randomized approximation of linear functionals on function spaces

- Mathematics, Computer ScienceQuantum Inf. Process.
- 2011

Lower bounds are provided on the power of quantum, randomized and deterministic algorithms for the exemplary problems, and some cases sharpness of the obtained results is compared.

### 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.

### 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).

### Quantum Approximation Error on Some Sobolev Classes

- Computer Science, PhysicsThird International Conference on Natural Computation (ICNC 2007)
- 2007

The results show that for p < q the quantum model of computation can bring a speedup of roughly squaring the rate of classical deterministic and randomized settings.

## References

SHOWING 1-9 OF 9 REFERENCES

### Quantum approximation I. Embeddings of finite-dimensional Lp spaces

- Mathematics, Computer ScienceJ. Complex.
- 2004

### 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.

### Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers

- Mathematics, Computer ScienceFound. Comput. Math.
- 2004

The worst case, randomized, and quantum settings are considered and it is proved that strong tractability and tractability in the class $\lall$ are equivalent and this holds under the same assumption as for the class £lall in the worst case setting.

### The finite element method for elliptic problems

- MathematicsClassics in applied mathematics
- 2002

From the Publisher:
This book is particularly useful to graduate students, researchers, and engineers using finite element methods. The reader should have knowledge of analysis and functional…

### Discretization of the problem of diameters

- Usp. Mat. Nauk 30, No. 6 (186)
- 1975