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
From Monte Carlo to quantum computation
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Visualization of the Quantum Fourier Transform Using a Quantum Computer Simulator
Quantum Information Processing
Quantum approximation I. Embeddings of finite-dimensional Lp spaces
Journal of Complexity
Simulation of entanglement generation and variation in quantum computation
Journal of Computational Physics
Automatic Synthesis of Composable Sequential Quantum Boolean Circuits
ICCD '05 Proceedings of the 2005 International Conference on Computer Design
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
The quantum query complexity of elliptic PDE
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms
Journal of Approximation Theory
A review of procedures to evolve quantum algorithms
Genetic Programming and Evolvable Machines
Quantum integration error for some sobolev classes
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Numerical analysis on a quantum computer
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Hybrid GF(2) --- boolean expressions ..for quantum computing circuits
RC'11 Proceedings of the Third international conference on Reversible Computation
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From the Publisher:The purpose of this monograph is to provide the mathematically literate reader with an accessible introduction to the theory of quantum computing algorithms, one component of a fascinating and rapidly developing area which involves topics from physics, mathematics, and computer science.The author briefly describes the historical context of quantum computing and provides the motivation, notation, and assumptions appropriate for quantum statics, a non-dynamical, finite dimensional model of quantum mechanics. This model is then used to define and illustrate quantum logic gates and representative subroutines required for quantum algorithms. A discussion of the basic algorithms of Simon and of Deutsch and Jozsa sets the stage for the presentation of Grover's search algorithm and Shor's factoring algorithm, key algorithms which crystallized interest in the practicality of quantum computers. A group theoretic abstraction of Shor's algorithms completes the discussion of algorithms.The last third of the book briefly elaborates the need for error-correction capabilities and then traces the theory of quantum error-correcting codes from the earliest examples to an abstract formulation in Hilbert space. This text 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. Readers interested in following the ongoing developments of quantum algorithms will benefit particularly from this presentation of the notation and basic theory.