Clifford-hierarchy stabilizer formalism with applications to twisted quantum doubles

arXiv:2610.00464 · quant-ph, cond-mat.str-el · Submitted 2026-09-30 · Read on arXiv

quant-ph, cond-mat.str-el

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Topological Order — 26× in this paper · explained in 2 episodes
• Anyons — 22× in this paper · explained in 2 episodes
• Stabilizer States — 19× in this paper · explained in 2 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Anyon Condensation — 1× in this paper · explained in 1 episode
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Distillation — 1× in this paper · explained in 2 episodes
• Domain Walls — 1× in this paper · explained in 2 episodes
• Topological Defects — 1× in this paper · explained in 2 episodes

Sources

• Quantum Error Correction via Codes over GF(4)
• Non-binary Unitary Error Bases and Quantum Codes
• An Introduction to Topological Quantum Codes
• Quantum codes on a lattice with boundary
• The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise
• Universal quantum computation in the surface code using non-Abelian islands
• Generating logical magic states with the aid of non-Abelian topological order
• Universal quantum computation with group surface codes
• Non-Abelian qLDPC: TQFT Formalism, Addressable Gauging Measurement and Application to Magic State Fountain on 2D Product Codes
• Fast magic state preparation by gauging higher-form transversal gates in parallel
• Non-Abelian Quantum Low-Density Parity Check Codes and Non-Clifford Operations from Gauging Logical Gates via Measurements
• Classification of topologically protected gates for local stabilizer codes
• A Non-Commuting Stabilizer Formalism
• Topological interactions in broken gauge theories
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases
• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Tube algebras, excitations statistics and compactification in gauge models of topological phases
• Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks

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