It is well-known that Shor's factorization algorithm, Simon's period-finding

algorithm, and Deutsch'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'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.