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

• URL: http://arxiv.org/abs/2503.15751v1
• Date: Wed, 19 Mar 2025 23:59:46 GMT
• Title: Universal fault tolerant quantum computation in 2D without getting tied in knots
• Authors: Margarita Davydova, Andreas Bauer, Julio C. Magdalena de la Fuente, Mark Webster, Dominic J. Williamson, Benjamin J. Brown,
• Abstract summary: We show how to perform fault-tolerant non-Clifford gates in two dimensions.<n>We formulate a path framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits.
• Score: 1.796950496605906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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