Topological Quantum Computation on Supersymmetric Spin Chains

• URL: http://arxiv.org/abs/2209.03822v1
• Date: Thu, 8 Sep 2022 13:52:10 GMT
• Title: Topological Quantum Computation on Supersymmetric Spin Chains
• Authors: Indrajit Jana, Filippo Montorsi, Pramod Padmanabhan and Diego Trancanelli
• Abstract summary: Quantum gates built out of braid group elements form the building blocks of topological quantum computation. We show that the fusion spaces of anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising ($k=2$), Fibonacci ($k=3$) and Jones-Kauffman ($k=4$) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group on the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing.

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