Graphical description of the action of local Clifford transformations on graph states

Nest, Maarten Van den; Dehaene, Jeroen; Moor, Bart De

doi:10.1103/physreva.69.022316

Cited by 267 publications

(467 citation statements)

References 7 publications

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“…local complementation of graphs [5][6][7][8] to the most studied MBQC architecture, namely the one-way quantum computer (1WQC) [2]. The resulting model preserves the advantages of 1WQC, while it relaxes the main obstacle toward its implementation.…”

Section: Introductionmentioning

confidence: 99%

Sequential measurement-based quantum computing with memories

et al. 2011

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We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the cluster state needed for the computation and its consumption by measurements are carried out simultaneously. As a consequence, effective clusters of one spatial dimension fewer than in the standard approach are sufficient for computation. In particular, universal computation requires only a one-dimensional array of memories. The scheme applies to discrete-variable systems of any dimension as well as to continuous-variable ones, and both are treated equivalently under the light of local complementation of graphs. In this way our formalism introduces a general framework that encompasses and generalizes in a unified manner some previous system-dependent proposals. The procedure is intrinsically well-suited for implementations with atom-photon interfaces.

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Section: Introductionmentioning

confidence: 99%

Sequential measurement-based quantum computing with memories

et al. 2011

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“…We have previously classified all self-dual additive codes over GF(4) of length up to 12 [8], by using the fact that all such codes can be represented as undirected graphs [3,10,20,23], and that an operation called local complementation (LC) generates orbits of graphs that correspond to equivalence classes of codes [3,23].…”

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confidence: 99%

Directed graph representation of half-rate additive codes over GF(4)

Danielsen

Parker

2010

Des. Codes Cryptogr.

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We show that (n, 2 n ) additive codes over GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive codes over GF(4), which correspond to undirected graphs. Graph representation reduces the complexity of code classification, and enables us to classify additive (n, 2 n ) codes over GF(4) of length up to 7. From this we also derive classifications of isodual and formally self-dual codes. We introduce new constructions of circulant and bordered circulant directed graph codes, and show that these codes will always be isodual. A computer search of all such codes of length up to 26 reveals that these constructions produce many codes of high minimum distance. In particular, we find new near-extremal formally self-dual codes of length 11 and 13, and isodual codes of length 24, 25, and 26 with better minimum distance than the best known self-dual codes.

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“…In fact, each additive curve represents a basis in the 2 n dimensional Hilbert space, so that the stabilizer state is one element of such basis. Not each curve can be directly associated with a graph state [70], but it can be reduced to an appropriate graph state through local Clifford transformations [71]. While the classification of the graph states represents a formidable task for large numbers of qubits, the phase-space approach allows working with algebraic structures.…”

Section: Curves Over Gf(2 3 )mentioning

confidence: 99%

Discrete phase-space structure of n-qubit mutually unbiased bases

et al. 2009

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We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2 n ) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four-and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for n qubits.

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Graphical description of the action of local Clifford transformations on graph states

Cited by 267 publications

References 7 publications

Sequential measurement-based quantum computing with memories

Sequential measurement-based quantum computing with memories

Directed graph representation of half-rate additive codes over GF(4)

Discrete phase-space structure of n-qubit mutually unbiased bases

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