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Springer eBooks

The Calculus of Full Quantum Logic

Peter Mittelstaedt

Published Jan 1, 1978• 0 citations
Publisher
DOI
10.1007/978-94-009-9871-1_7

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 13, 2000•0 citations
Recently we proved that there are two non-isomorphic models of the calculus of quantum logic corresponding to an infinite-dimensional Hilbert space representation: an orthomodular lattice and a weakly orthomodular lattice. We also discovered that there are two non-isomorphic models of the calculus of classical logic: a distributive lattice (Boolean algebra) and a weakly distributive lattice. In this work we consider implications of these results to a quantum simulator which should mimic quantum systems by giving precise instructions on how to produce input state, how to evolve them, and how to read off the final states. We analyze which conditions quantum states of a quantum computer currently obey and which they should obey in order to enable full quantum computing, i.e., proper quantum mathematics. In particular we find several new conditions which lattices of Hilbert space subspaces must satisfy.