QuEnG Seminar || Quantum Computing - “AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states”

on the March 10, 2021

At 2:00pm
We are pleased to restart the Quantum Computing seminars for 2021. These seminars cover all aspects of quantum computing and quantum information theory, and will be jointly organised with the quantum information community in Lyon.
Our first seminar for 2021 will be given by Richard East from the UGA and Institut Néel, on Wednesday 10 March at 2pm on Zoom (link below).

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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ID de réunion : 992 6827 9193
Code secret : 734348
Published on March 5, 2021

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