Mapping graph state orbits under local complementation

@article{Adcock2020MappingGS,
  title={Mapping graph state orbits under local complementation},
  author={Jeremy C Adcock and Sam Morley-Short and Axel Dahlberg and Joshua W. Silverstone},
  journal={Quantum},
  year={2020},
  volume={4},
  pages={305}
}
Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data… 

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References

SHOWING 1-10 OF 48 REFERENCES
MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES
TLDR
The one-way quantum computer is described, a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state, which proves the universality of the , and establishes the link to the network model — the common model of quantum computation.
Counting single-qubit Clifford equivalent graph states is #P-Complete
TLDR
This paper considers the computational complexity of, given a graph state |G>, counting the number of graph states, single-qubit Clifford equivalent to |G>.
Generation of time-domain-multiplexed two-dimensional cluster state
TLDR
Generating a large-scale two-dimensional continuous-variable cluster state that is compatible with Bosonic error-correcting codes that enable fault-tolerant quantum computation and readily scalable and fault tolerant.
Entanglement in Graph States and its Applications
TLDR
This review gives a tutorial introduction into the theory of graph states, and discusses the basic notions and properties of these states, including aspects of non-locality, bi-partite and multi- partite entanglement and its classification in terms of the Schmidt measure.
Graphical description of the action of local Clifford transformations on graph states
We translate the action of local Clifford operations on graph states into transformations on their associated graphs, i.e., we provide transformation rules, stated in purely graph theoretical terms,
Schmidt measure as a tool for quantifying multiparticle entanglement
We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the
Multiparty entanglement in graph states
TLDR
This work characterize and quantify the genuine multiparticle entanglement of such graph states in terms of the Schmidt measure, to which it provides upper and lower bounds in graph theoretical terms.
Time-Domain Multiplexed 2-Dimensional Cluster State: Universal Quantum Computing Platform
TLDR
For the first time among any physical system, experimental realization of a scalable resource state for universal MBQC: a 2-dimensional cluster state based on time-domain multiplexing approach that allows unlimited resource generation regardless of the coherence time of the system is presented.
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