@article {1314, title = {Quantum computation from a quantum logical perspective}, year = {2006}, month = {2006/05/29}, abstract = { It is well-known that Shor{\textquoteright}s factorization algorithm, Simon{\textquoteright}s period-finding algorithm, and Deutsch{\textquoteright}s original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the information-processing in the three algorithms are presented from a different perspective, in terms of the way in which the algorithms exploit the non-Boolean quantum logic represented by the projective geometry of Hilbert space. From this quantum logical perspective, the XOR algorithm appears directly as a special case of Simon{\textquoteright}s algorithm, and all three algorithms can be seen as exploiting the non-Boolean logic represented by the subspace structure of Hilbert space in a similar way. Essentially, a global property of a function (such as a period, or a disjunctive property) is encoded as a subspace in Hilbert space representing a quantum proposition, which can then be efficiently distinguished from alternative propositions, corresponding to alternative global properties, by a measurement (or sequence of measurements) that identifies the target proposition as the proposition represented by the subspace containing the final state produced by the algorithm. }, url = {http://arxiv.org/abs/quant-ph/0605243v2}, author = {Jeffrey Bub} }