Holographic Software for Quantum Networks

Abstract

We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to translate between a topological approach and an algebraic approach. Using our software, we give a topological simulation for quantum networks. The string Fourier transform (SFT) is our basic tool to transform product states into states with maximal entanglement entropy. We obtain a pictorial interpretation of Fourier transformation, of measurements, and of local transformations, including the $n$-qudit Pauli matrices and their representation by Jordan-Wigner transformations. We use our software to discover interesting new protocols for multipartite communication. In summary, we build a bridge linking the theory of planar para algebras with quantum information.

48 pages. Accepted for publication in SCIENCE CHINA Mathematics

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• Non-Abelian Anyons and Topological Quantum Computation
• The Quantum Internet
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Cited by in corpus (8)

• Quantum scrambling with classical shadows
• Quantum Fourier Analysis
• Classical simulation of quantum circuits by half Gauss sums
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Quantum teleportation in the commuting operator framework
• De Finetti Theorems for Braided Parafermions
• Zigzag normalisation for associative $n$-categories
• The planar parafermion algebra: The ${\mathbb{Z}}_N$ clock model and the coupled Temperley-Lieb algebra