Book contents
- Frontmatter
- Contents
- Introduction
- Part I Quantum information
- Part II Quantum computation
- 7 Principles of quantum computing
- 8 Elementary quantum algorithms
- 9 More advanced quantum algorithms
- 10 Trapped atoms and ions
- 11 Nuclear magnetic resonance
- 12 Large-scale quantum computers
- Part III Quantum communication
- Appendix: Quantum mechanics
- References
- Index
9 - More advanced quantum algorithms
from Part II - Quantum computation
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Introduction
- Part I Quantum information
- Part II Quantum computation
- 7 Principles of quantum computing
- 8 Elementary quantum algorithms
- 9 More advanced quantum algorithms
- 10 Trapped atoms and ions
- 11 Nuclear magnetic resonance
- 12 Large-scale quantum computers
- Part III Quantum communication
- Appendix: Quantum mechanics
- References
- Index
Summary
Deutsch's algorithm and Grover's quantum search are theoretically interesting, but it is not obvious that these two algorithms are actually useful for anything important. We next consider a selection of more advanced algorithms, several of which may have real-life applications. Some of these will be too complicated to explain fully, and their properties will only be sketched briefly.
The Deutsch–Jozsa algorithm
Deutsch's algorithm is simple, but important, as it shows that a quantum algorithm can find a property of an unknown function (its parity) with a smaller number of queries than any possible classical algorithm (one rather than two). For this reason we can say that quantum computing is more efficient than classical computing within the oracle model of function evaluation. (It is widely believed that quantum computing is more efficient than classical computing in general, but this is a surprisingly hard thing to prove.) The simplicity of the algorithm is also an advantage, as it can be implemented on very primitive quantum computers. Beyond this, however, Deutsch's algorithm is also important as the simplest member of a large family of quantum algorithms, including most notably Shor's quantum factoring algorithm.
The second simplest algorithm in the family is the Deutsch–Jozsa algorithm, which solves a very closely related problem. Consider an unknown binary function with n input bits, giving N = 2n possible inputs, and a single output bit.
- Type
- Chapter
- Information
- Quantum Information, Computation and Communication , pp. 85 - 98Publisher: Cambridge University PressPrint publication year: 2012