Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reversibility in the Extended Measurement-based Quantum Computation   When applied on some particular quantum entangled states, measurements are
universal for quantum computing. In particular, despite the fondamental
probabilistic evolution of quantum measurements, any unitary evolution can be
simulated by a measurement-based quantum computer (MBQC). We consider the
extended version of the MBQC where each measurement can occur not only in the
(X,Y)-plane of the Bloch sphere but also in the (X,Z)- and (Y,Z)-planes. The
existence of a gflow in the underlying graph of the computation is a necessary
and sufficient condition for a certain kind of determinism. We extend the
focused gflow (a gflow in a particular normal form) defined for the (X,Y)-plane
to the extended case, and we provide necessary and sufficient conditions for
the existence of such normal forms.

25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int