Cluster
states, algorithms and graphs
(pp287-324)
D. Schlingemann
doi:
https://doi.org/10.26421/QIC4.4-4
Abstracts:
The present paper is concerned with the concept of the
one-way quantum computer, beyond binary-systems, and its relation to the
concept of stabilizer quantum codes. This relation is exploited to
analyze a particular class of quantum algorithms, called graph
algorithms, which correspond in the binary case to the Clifford group
part of a network and which can efficiently be implemented on a one-way
quantum computer. These algorithms can ``completely be solved" in the
sense that the manipulation of quantum states in each step can be
computed explicitly. Graph algorithms are precisely those which
implement encoding schemes for graph codes. Starting from a given
initial graph, which represents the underlying resource of multipartite
entanglement, each step of the algorithm is related to a explicit
transformation on the graph.
Key words:
cluster states, graph states, quantum error correction, algorithms,
one-way quantum computing |