10,519 research outputs found
GEMs and amplitude bounds in the colored Boulatov model
In this paper we construct a methodology for separating the divergencies due
to different topological manifolds dual to Feynman graphs in colored group
field theory. After having introduced the amplitude bounds using propagator
cuts, we show how Graph-Encoded-Manifolds (GEM) techniques can be used in order
to factorize divergencies related to different parts of the dual topologies of
the Feynman graphs in the general case. We show the potential of the formalism
in the case of 3-dimensional solid torii in the colored Boulatov model.Comment: 20 pages; 20 Figures; Style changed, discussion improved and typos
corrected, citations added; These GEMs are not related to "Global Embedding
Minkowskian spacetimes
The Small Stellated Dodecahedron Code and Friends
We explore a distance-3 homological CSS quantum code, namely the small
stellated dodecahedron code, for dense storage of quantum information and we
compare its performance with the distance-3 surface code. The data and ancilla
qubits of the small stellated dodecahedron code can be located on the edges
resp. vertices of a small stellated dodecahedron, making this code suitable for
3D connectivity. This code encodes 8 logical qubits into 30 physical qubits
(plus 22 ancilla qubits for parity check measurements) as compared to 1 logical
qubit into 9 physical qubits (plus 8 ancilla qubits) for the surface code. We
develop fault-tolerant parity check circuits and a decoder for this code,
allowing us to numerically assess the circuit-based pseudo-threshold.Comment: 19 pages, 14 figures, comments welcome! v2 includes updates which
conforms with the journal versio
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