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

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arxiv 2503.15751 v2 pith:A3R6V6KP submitted 2025-03-19 quant-ph cond-mat.str-el

Margarita Davydova , Andreas Bauer , Julio C. Magdalena de la Fuente , Mark Webster , Dominic J. Williamson , Benjamin J. Brown This is my paper · ORCID
classification quant-phcond-mat.str-el
keywords codenon-abeliangatestopologicalactionapproacharrayassociated
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finding diagonal logical gates in CSS codes and circuits

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Diagonal logical gates of a CSS code or circuit are exactly the kernel of a pullback map on phase functions, and that kernel can be computed in cubic time.

  2. Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes

    quant-ph 2025-12 conditional novelty 7.0 of 10

    Non-Abelian surface codes based on dihedral groups D_{4N} implement transversal phase gates T^{1/N} at any Clifford-hierarchy level in 2D, with a qubit-only version when 8N is a power of two.

  3. Efficient simulation of logical magic state preparation protocols

    quant-ph 2025-12 conditional novelty 6.0 of 10

    A classical simulation method that propagates circuit-level Pauli noise to a Clifford error makes logical magic-state preparation protocols simulable in time polynomial in qubits and the target state's stabilizer rank.

  4. Non-Clifford gates between stabilizer codes via non-Abelian topological order

    quant-ph 2025-05 conditional novelty 6.0 of 10

    A protocol uses the non-Abelian S3 quantum double as an intermediate to implement a controlled charge-conjugation (CC) gate between qubit and qutrit surface codes.

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