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Qudit lattice surgery
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abstract
We observe that lattice surgery, a model of fault-tolerant qubit computation, generalises straightforwardly to arbitrary finite-dimensional qudits. The generalised model is based on the group algebras $\mathbb{C}\mathbb{Z}_d$ for $d \geq 2$. It still requires magic state injection for universal quantum computation. We relate the model to the ZX-calculus, a diagrammatic language based on Hopf-Frobenius algebras.
Forward citations
Cited by 3 Pith papers
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Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes
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.
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Non-Abelian dynamics on a cube: improving quantum compilation through qudit-based simulations
A qudit-based circuit for SU(2) lattice gauge theory on a cube, with improved decompositions for uniformly-controlled rotations and new elementary-gate resource estimates.
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Generating logical magic states with the aid of non-Abelian topological order
A new protocol uses gauging and anyon condensation through the D4 quantum double model to produce a logical magic state in the Z2 surface code from a Clifford state in the Z4 surface code.
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