Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum computation from a quantum logical perspective   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.

26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph