AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
In: EISSN: 2691-3399 ; PRX Quantum ; https://hal.science/hal-03047342 ; PRX Quantum, 2022, 2022
academicJournal
Zugriff:
21 pages, 5 figures ; International audience ; From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalysed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation, but cannot generally be computed with directly. In this paper we introduce the ZXH-calculus, a graphical language based on the ZX-calculus, that we use to represent and reason about many-body states entirely graphically. As a demonstration, we express the 1D AKLT state, a symmetry protected topological state, in the ZXH-calculus by developing a representation of spins higher than 1/2 within the calculus. By exploiting the simplifying power of the ZXH-calculus rules we show how this representation straightforwardly recovers two important properties, the existence of topologically protected edge states, and the non-vanishing of a string order parameter. We furthermore show how the AKLT matrix-product state representation can be recovered from our diagrams. In addition, we provide an alternative proof that the 2D AKLT state on a hexagonal lattice can be reduced to a graph state, demonstrating that it is a universal quantum computing resource. Our results show that the ZXH-calculus is a powerful language for representing and computing with physical states entirely graphically, paving the way to develop more efficient many-body algorithms.
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AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
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Autor/in / Beteiligte Person: | East, Richard D. P. ; van de Wetering, John ; Chancellor, Nicholas ; Grushin, Adolfo G. ; Nanophysique et Semiconducteurs (NEEL - NPSC) ; Institut Néel (NEEL) ; Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ) ; Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ) ; Université Grenoble Alpes (UGA) ; Laboratoire d'Informatique de Grenoble (LIG) ; Radboud University Nijmegen ; Department of Physics Durham ; University of New Hampshire (UNH) ; Théorie de la Matière Condensée (NEEL - TMC) ; EP/S00114X/1, EPSRC ; ANR-18-CE30-0001,Topodrive,Effets linéaires et non linéaires dans les matériaux topologiques irradiés(2018) |
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Zeitschrift: | EISSN: 2691-3399 ; PRX Quantum ; https://hal.science/hal-03047342 ; PRX Quantum, 2022, 2022 |
Veröffentlichung: | HAL CCSD ; APS Physics, 2022 |
Medientyp: | academicJournal |
DOI: | 10.1103/PRXQuantum.3.010302 |
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