## Quantum Computing: A new Paradigm and it's Type Theory (1996)

Venue: | Lecture given at the Quantum Computing Seminar, Lehrstuhl Prof. Beth, Universität |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Wehr96quantumcomputing:,

author = {Martin Wehr},

title = {Quantum Computing: A new Paradigm and it's Type Theory},

booktitle = {Lecture given at the Quantum Computing Seminar, Lehrstuhl Prof. Beth, Universität},

year = {1996}

}

### OpenURL

### Abstract

To use quantum mechanical behavior for computing has been proposed by Feynman. Shor gave an algorithm for the quantum computer which raised a big stream of research. This was because Shor's algorithm did reduce the yet assumed exponential complexity of the security relevant factorization problem, to a quadratic complexity if quantum computed. In the paper a short introduction to quantum mechanics can be found in the appendix. With this material the operation of the quantum computer, and the ideas of quantum logic will be explained. The focus will be the argument that a connection of quantum logic and linear logic is the right type theory for quantum computing. These ideas are inspired by Vaughan Pratt's view that the intuitionistic formulas argue about states (i.e physical quantum states) and linear formulas argue about state transformations (i.e computation steps). 1 Introduction A calculus for programs on quantum computers is strongly missed. Here we present the material t...

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Citation Context ...ics the set theory. So implication A ! B will be interpreted as the set of all maps from set A to set B, the typing relation e : A becomes the element relation 2 in set theory. It was Milners idea in =-=[Mil78]-=- to observe, if we insert in every set the element W rong and interpret impossible operations (for instance application to a constant 1e) as W rong, then the principle of type theory well typed progra... |

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