Non-Clifford Gates via Non-Abelian Topological Orders
ORAL
Abstract
A critical mission for realizing large-scale quantum computing is the development of simple and resource-efficient implementations of logical non-Clifford gates. This talk discusses how topological field theory enables novel protocols for their implementation.
In the first part, based on arXiv:2510.20890, we present hybrid lattice surgery between Abelian and non-Abelian codes and show how it provides non-Clifford operations in the standard surface code, including non-Clifford gates and magic states, for qubits and qutrits.
In the second part, based on arXiv:2512.13777, we provide a purely 2D transversal realization of non-Clifford qubit phase gates at arbitrary levels of the Clifford hierarchy. We encode a logical qubit in the quantum double of a non-Abelian group on a triangular spatial patch and implement the logical gate transversally by stacking a symmetry-protected topological (SPT) phase onto the spatial region. This construction remains purely 2D and preserves locality and fault tolerance.
In the first part, based on arXiv:2510.20890, we present hybrid lattice surgery between Abelian and non-Abelian codes and show how it provides non-Clifford operations in the standard surface code, including non-Clifford gates and magic states, for qubits and qutrits.
In the second part, based on arXiv:2512.13777, we provide a purely 2D transversal realization of non-Clifford qubit phase gates at arbitrary levels of the Clifford hierarchy. We encode a logical qubit in the quantum double of a non-Abelian group on a triangular spatial patch and implement the logical gate transversally by stacking a symmetry-protected topological (SPT) phase onto the spatial region. This construction remains purely 2D and preserves locality and fault tolerance.
*This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award No. DE-SC0026209. The work of S-JH, SSN and AW is supported by the UKRI Frontier Research Grant, underwriting the ERC Advanced Grant "Generalized Symmetries in Quantum Field Theory and Quantum Gravity". This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics.
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Publication: Title: Hybrid Lattice Surgery: Non-Clifford Gates via Non-Abelian Surface Codes
Authors: Sheng-Jie Huang; Alison Warman; Sakura Schafer-Nameki; Yanzhu Chen
arXiv:2510.20890
Presenters
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Alison Warman
- University of Oxford