Topological Quantum Computation on Supersymmetric Spin Chains

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.

56 pages, 17 figures, v2 to appear in JHEP. Includes stability analysis

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
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• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
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• Spin chains with dynamical lattice supersymmetry
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Cited by in corpus (2)

• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry