Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamentals of universality in one-way quantum computation   We build a framework allowing for a systematic investigation of the issue:
"Which quantum states are universal resources for one-way quantum computation?"
We start by re-examining what is exactly meant by "universality" in quantum
computation, and what the implications are for universal one-way quantum
computation. Given the framework of a measurement-based quantum computer, where
quantum information is processed by local operations only, the most general
universal one-way quantum computer is one which is capable of accepting
arbitrary classical inputs and producing arbitrary quantum outputs--we refer to
this property as CQ-universality. We then show that a systematic study of
CQ-universality in one-way quantum computation is possible by identifying
entanglement features that must be present in every universal resource. These
insights are used to identify several states as being not universal, such as 1D
cluster states, W states, and ground states of non-critical 1D spin systems.
Our criteria are strengthened by considering the efficiency of a quantum
computation, and we find that entanglement measures must obey a certain scaling
law with the system size for all efficient universal resources. This again
leads to examples of non-universal resources, such as, e.g., ground states of
critical 1D spin systems. We also provide several examples of efficient
universal resources, namely graph states corresponding to hexagonal, triangular
and Kagome lattices. Finally, we consider the more general notion of encoded
CQ-universality, where quantum outputs are allowed to be produced in an encoded
form. Again we provide entanglement-based criteria for encoded universality.
Moreover, we present a general procedure to construct encoded universal
resources.

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The categories of this paper are: cs
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph