## 47 Citations

### Quantum integration error for some sobolev classes

- Computer Science
- 2006

It is proved that for these classes of functions the optimal convergence rates of quantum algorithms are essential smaller than those of classical deterministic and randomized algorithms.

### 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 Integration Error on Some Classes of Multivariate Functions

- Mathematics, Computer ScienceICIC
- 2007

The results show that for these two type of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.

### 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.

### Lower bound for quantum integration error on anisotropic Sobolev classes

- Mathematics, Computer Science
- 2010

The results show that for anisotropic Hölder-Nikolskii and Sobolev classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.

### Information-Based Complexity of Integration in the Randomized and Quantum Computation Model

- Computer Science, Mathematics
- 2011

The integration of the Hölder-Nikolskii classes in the randomized and quantum computation model is investigated and it is seen that quantum computing can reach an exponential speed up over deterministic classical computation and a quadratic speedup over randomized classical computation.

### 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.

## References

SHOWING 1-10 OF 21 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.

### 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…

### Path Integration on a Quantum Computer

- Computer ScienceQuantum Inf. Process.
- 2002

A lower bound is obtained for the minimal number of quantum queries which shows that this bound cannot be significantly improved, and it is proved that path integration on a quantum computer is tractable.

### A framework for fast quantum mechanical algorithms

- Computer Science, PhysicsSTOC '98
- 1998

The sqrt(N) step quantum search algorithm is an immediate consequence of a framework for the design and analysis of quantum mechanical algorithms, and several other search-type applications are presented.

### 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.

### Quantum Complexity of Integration

- Computer Science, MathematicsJ. Complex.
- 2001

It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the…

### 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…

### Algorithms for quantum computation: discrete logarithms and factoring

- Computer ScienceProceedings 35th Annual Symposium on Foundations of Computer Science
- 1994

Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.