Ben Brown (@benbrown.bsky.social)

Logic gates can often be understood in terms of topological phases, so I often felt it was a shortcoming of my work on a 2D CCZ gate that I did not see the analogous physical picture. So I am pleased to share our work arxiv.org/abs/2503.15751 where we show the gate was a non-Abelian phase all along!

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Universal fault tolerant quantum computation in 2D without getting tied in knots 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. https://arxiv.org/abs/2503.15751