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arXiv · 2503.15751

Universal fault tolerant quantum computation in 2D without getting tied in knots

Margarita Davydova·Andreas Bauer·Julio C. Magdalena de la Fuente·Mark Webster·Dominic J. Williamson·Benjamin J. Brown
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Abstract

We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a path integral framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits. We also show an equivalence between our approach and prior proposals where a 2D array of qubits reproduces the action of a transversal gate in a 3D stabilizer code over time, thus, establishing a new connection between 3D codes and 2D non-Abelian topological phases. We prove a threshold theorem for our protocols under local stochastic circuit noise using a just-in-time decoder to correct the non-Abelian code.

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Margarita Davydova, Andreas Bauer, Julio C. Magdalena de la Fuente, Mark Webster, Dominic J. Williamson, Benjamin J. Brown. 2025-03-19. Universal fault tolerant quantum computation in 2D without getting tied in knots. https://doi.org/10.1103/vrty-qs5h

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