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Topological Quantum Computation
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abstract
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possibility for the realization of quantum computers. The chief advantage of anyonic computation would be physical error correction: An error rate scaling like $e^{-\a\l}$, where $\l$ is a length scale, and $\alpha$ is some positive constant. In contrast, the $\q$presumptive" qubit-model of quantum computation, which repairs errors combinatorically, requires a fantastically low initial error rate (about $10^{-4}$) before computation can be stabilized.
Forward citations
Cited by 5 Pith papers
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Microscopic universal theory of symmetry-enriched topological quantum spin liquids
A new framework maps microscopic inputs to universal properties of generic symmetry-enriched TQSLs and establishes a bijective crystalline equivalence principle between lattice-plus-internal and internal-only symmetry data.
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Irrational CFTs from coupled anyon chains with non-invertible symmetries?
DMRG evidence from three coupled Fibonacci anyon chains points to a conformal phase with c=2.10±0.03, proposed as a candidate irrational CFT, though small system sizes leave a weakly first-order alternative open.
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Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta
Fractional quantum Hall anyons are re-derived from a non-Lagrangian flux quantization in 2-Cohomotopy, with new predictions for torus degeneracy and defect anyons.
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Engineering of Anyons on M5-Probes via Flux Quantization
Flux quantization of the M5-brane tensor field in twisted Cohomotopy yields Pontrjagin homology observables that reproduce abelian Chern-Simons theory and braid actions on defect anyons.
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Tables of practical invariants for distinguishing multiplicity-free fusion categories up to rank 7
For every multiplicity-free fusion ring up to rank 7, a table of small invariants distinguishes all inequivalent pivotal braided and non-braided fusion categories in the Anyonica census.
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