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Quantum and non-signalling graph isomorphisms
2018
Journal of combinatorial theory. Series B (Print)
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We then define the notions of quantum and non-signalling isomorphism, by considering perfect quantum and non-signalling strategies for the (G, H)-isomorphism game, respectively. ...
When such an isomorphism exists, we say that G and H are isomorphic and write G ∼ = H. The graph isomorphism (GI) problem consists of deciding whether two graphs are isomorphic. ...
From this it follows that quantum and non-signalling isomorphism are different: Corollary 5.12. There exist graphs that are non-signalling isomorphic but not quantum isomorphic. ...
doi:10.1016/j.jctb.2018.11.002
fatcat:o3r5m4737fdi7mkdiuuzpihcmi
Quantum and non-signalling graph isomorphisms
[article]
2017
arXiv
pre-print
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We then define the notions of quantum and non-signalling isomorphism, by considering perfect quantum and non-signalling strategies for the (G,H)-isomorphism game, respectively. ...
We introduce a two-player nonlocal game, called the (G,H)-isomorphism game, where classical players can win with certainty if and only if the graphs G and H are isomorphic. ...
From this it follows that quantum and non-signalling isomorphism are different: Corollary 5.11. There exist graphs that are non-signalling isomorphic but not quantum isomorphic. ...
arXiv:1611.09837v3
fatcat:vayzru5tgvb57f4wrr45vwqonq
Quantum Graph Neural Networks
[article]
2019
arXiv
pre-print
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clustering, and supervised learning for graph isomorphism classification. ...
We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable ...
GV, EL, and VS would like to thank the team at X for the hospitality and support during their respective Quantum@X and AI@X residencies where this work was completed. ...
arXiv:1909.12264v1
fatcat:tnovpmgworfwdd6qgp5hw4cexa
On quantum invariants and the graph isomorphism problem
[article]
2019
arXiv
pre-print
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The performance of these invariants is evaluated and compared to classical invariants. We verify that the invariants can distinguish all non-isomorphic graphs with 9 or fewer nodes. ...
Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. ...
The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Q experience team. R.P.R. is funded by the EPSRC [grant number EP/N509516/1]. ...
arXiv:1711.09842v3
fatcat:t7diwdj2irfaxlqd6h2wkgzcsi
Quantum symmetry vs nonlocal symmetry
[article]
2021
arXiv
pre-print
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We investigate the differences and similarities between this and the notion of quantum symmetry, defined as non-commutativity of C(Qut(G)). ...
Roughly speaking, quantum symmetry vs nonlocal symmetry can be viewed respectively as non-classicality of our model of reality vs non-classicality of our observation of reality. ...
SS: Supported by the EPSRC project "Quantum groups in action", EP/T03064X/1 and the DFG project "Quantenautomorphismen von Graphen". ...
arXiv:2012.13328v2
fatcat:bh6swy5r6zga7hgrlyj7btynm4
STRUCTURAL THEORY OF SPACE-TIME AND INTRAPOINT SYMMETRY
[chapter]
1989
Symmetry 2
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The paper presents the space-time theory, based on identifying non-geometrical intrapoint structure and symmetry. ...
It is shown that the structure defines topological (three-dimensionality, continuity, cohesion) and symmetrical (homogeneity, isotropy) characteristics of space and their relationship with the multilevel ...
Intrapoint symmetry is so none other but the statically considered non-geometrical structure of the quantum of light generated by three other types of light signals: p-, r+-and r_-signals. ...
doi:10.1016/b978-0-08-037237-2.50026-x
fatcat:rtsnbprrdrcu5oeaojvnicv7bm
Structural theory of space-time and intrapoint symmetry
1989
Computers and Mathematics with Applications
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The paper presents the space-time theory, based on identifying non-geometrical intrapoint structure and symmetry. ...
It is shown that the structure defines topological (three-dimensionality, continuity, cohesion) and symmetrical (homogeneity, isotropy) characteristics of space and their relationship with the multilevel ...
Intrapoint symmetry is so none other but the statically considered non-geometrical structure of the quantum of light generated by three other types of light signals: p-, r+-and r_-signals. ...
doi:10.1016/0898-1221(89)90163-6
fatcat:upxs3vixfrfczpejcndx5zddqq
Tribonacci Quantum Cosmology: Optimal Non-Antipodal Spherical Codes & Graphs
2019
Journal of Quantum Information Science
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Degrees of freedom in deep learning, quantum cosmological, information processing are shared and evolve through a self-organizing sequence of optimal , non-antipodal , spherical codes, . ...
These shared dimensions are conformed dimensions in computer science, which ensure consistency between Nature's quantum information processing of its physics at macro, meso and microscopic scales; and ...
Acknowledgements This original research is self-funded and I thank my reviewers and editors for their valuable support. ...
doi:10.4236/jqis.2019.91004
fatcat:w3zkitwenjcw3n2sgb23hgv3y4
Numerical Investigation of High-Purity Polarization-Entangled Photon-Pair Generation in Non-Poled KTP Isomorphs
2021
Applied Sciences
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between the interacting photons in non-poled crystals rather than periodically poled (PP) KTPs that are widely used for quantum experiments. ...
We investigated the high-purity entangled photon-pair generation in five kinds of "non-poled" potassium titanyl phosphate (KTP) isomorphs (i.e., KTiOPO4, RbTiOPO4, KTiOAsO4, RbTiOAsO4, and CsTiOAsO4). ...
Since KTP isomorphs have been commercialized as high-level crystal growth techniques, quantum light sources based on non-poled KTP isomorphs have good potential for fiber-optic and free-space quantum communication ...
doi:10.3390/app11020565
fatcat:32iuivqk3vgezhvanhuhljxogm
Graph isomorphism: Physical resources, optimization models, and algebraic characterizations
[article]
2020
arXiv
pre-print
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verifier that two graphs G and H are isomorphic. ...
In recent work along with Atserias, Šámal and Severini [Journal of Combinatorial Theory, Series B, 136:89–328, 2019] we showed that a verifier can be convinced that two non-isomorphic graphs are isomorphic ...
Motivated by this, in the previous work [1] we introduced the notions quantum and non-signalling isomorphisms of graphs in terms of the existence of perfect quantum and non-signalling strategies for ...
arXiv:2004.10893v1
fatcat:wnophwxi5jbhbcf4msnn56co3u
Synchronous games with *-isomorphic game algebras
[article]
2021
arXiv
pre-print
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We establish several strong equivalences of synchronous non-local games, in the sense that the corresponding game algebras are *-isomorphic. ...
As a result, we show that there are bisynchronous games with equal question and answer sets, whose optimal strategies only exist in the quantum commuting model, and not in the quantum approximate model ...
We would like to thank Michael Brannan, Matt Kennedy, Vern Paulsen, Connor Paddock, and William Slofstra for valuable discussions. ...
arXiv:2109.04859v1
fatcat:hp4444m5wbejjarbrizki3oh34
A quantum causal discovery algorithm
2018
npj Quantum Information
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2017 pre-print arXiv:1704.00800v1 fatcat:sd6omiw4kraspn5ldcjaohb2muOther Versions
Our algorithm determines whether the process is causally ordered by grouping the events into causally-ordered non-signaling sets. ...
For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. ...
This work was supported by the Australian Research Council (ARC) Centre of Excellence for Quantum Engineered Systems grant (CE 110001013), the ARC Centre for Quantum Computation and Communication Technology ...
doi:10.1038/s41534-018-0062-6
fatcat:qw4lobyvsvghnamgiqu2wbgxfi
Algorithms for Quantum Systems - Quantum Algorithms
[chapter]
2005
Quantum Information Processing
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All four graphs yield equivalent QECC, but the graphs are non-isomorphic. ...
Figure 1 . 1 : 11 Non-isomorphic graphs which all yield graphical quantum codes that are equivalent to the CSS code [[7, 1, 3]]. ...
doi:10.1002/3527603549.ch1
fatcat:4sshv4jhw5aq3fjnmqviyownvi
Algorithms for Quantum Systems - Quantum Algorithms
[chapter]
2005
Quantum Information Processing
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All four graphs yield equivalent QECC, but the graphs are non-isomorphic. ...
Figure 1 . 1 : 11 Non-isomorphic graphs which all yield graphical quantum codes that are equivalent to the CSS code [[7, 1, 3]]. ...
doi:10.1002/3527606009.ch1
fatcat:miu7yw6qtrdkrkrkiay5kyy6ru
Perfect strategies for non-signalling games
[article]
2018
arXiv
pre-print
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, many games based on graphs, and unique games. ...
We unify and consolidate various results about non-signall-ing games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general ...
We now recall the connection between non-signalling correlations and perfect strategies for non-signalling games. ...
arXiv:1804.06151v1
fatcat:7ipwswp7v5f5bkaov5vpzkfsxq
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