aqora

Anyons associated with the generalized braid groups

Takashi Yamamoto

Letters in Mathematical PhysicsAug 1, 19942 citations

Simulation of Anyons Using Symmetric Tensor Network Algorithms

Robert N. C. Pfeifer

In this thesis I develop a formalism whereby a tensor network may be understood in terms of a unitary braided tensor category, and represented in a particularly efficient manner corresponding to the exploitation of this mathematical structure. This approach permits the exploitation of the global Abelian and non-Abelian internal group symmetries of a lattice model, both to facilitate the study of particular symmetry sectors and to provide a considerable reduction in computational cost. It also enables the study of models with non-trivial exchange statistics (fermions, Abelian and non-Abelian anyons) using tensor network algorithms which scale polynomially in the system size.In this thesis I develop a formalism whereby a tensor network may be understood in terms of a unitary braided tensor category, and represented in a particularly efficient manner corresponding to the exploitation of this mathematical structure. This approach permits the exploitation of the global Abelian and non-Abelian internal group symmetries of a lattice model, both to facilitate the study of particular symmetry sectors and to provide a considerable reduction in computational cost. It also enables the study of models with non-trivial exchange statistics (fermions, Abelian and non-Abelian anyons) using tensor network algorithms which scale polynomially in the system size.

arXiv:1202.1522Feb 7, 20126 citations

Braiding anyons and communication between topological and non-topological systems

Haitan Xu, Jacob M. Taylor

Bulletin of the American Physical SocietyFeb 28, 20120 citations

Simulation of anyons with tensor network algorithms

Robert N. C. Pfeifer, Philippe Corboz, Oliver Buerschaper +3 more

Interacting systems of anyons pose a unique challenge to condensed-matter simulations due to their nontrivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons and demonstrate this process for the one-dimensional multiscale entanglement renormalization ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ans\"atze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.Interacting systems of anyons pose a unique challenge to condensed-matter simulations due to their nontrivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons and demonstrate this process for the one-dimensional multiscale entanglement renormalization ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ans\"atze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.

arXiv:1006.3532Physical Review BSep 29, 201056 citations

Computations in quantum tensor networks

Thomas Huckle, Konrad Waldherr, Thomas Schulte‐Herbrüggen

arXiv:1212.5005Linear Algebra and its ApplicationsJan 27, 201257 citations

E8 Phi‑Harmonic Fractal Anyon Tensor Network (PHFATTN) — E8 Intelligence Research

Andrew Stewart Caldin

The 240 root vectors of the E8 lattice organize into fifteen 16‑node clusters that, when driven at the 132 Hz phi‑harmonic, generate a self‑similar spectral flow through the Chern‑Simons Hilbert space, creating a hierarchical fractal anyon condensation. This fractal hierarchy yields a tensor network of non‑Abelian anyonic exchange paths whose connectivity mirrors the golden‑ratio geometry, endowing each braiding operation with an intrinsic multi‑level error‑correcting code that raises the logical qubit code distance exponentially with depth. Consequently, PHFATTN provides a scalable, fault‑tolerant quantum computing substrate where logical gates are executed deterministically by exploiting the E8 lattice's geometric symmetry and phase‑locked spectral dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comThe 240 root vectors of the E8 lattice organize into fifteen 16‑node clusters that, when driven at the 132 Hz phi‑harmonic, generate a self‑similar spectral flow through the Chern‑Simons Hilbert space, creating a hierarchical fractal anyon condensation. This fractal hierarchy yields a tensor network of non‑Abelian anyonic exchange paths whose connectivity mirrors the golden‑ratio geometry, endowing each braiding operation with an intrinsic multi‑level error‑correcting code that raises the logical qubit code distance exponentially with depth. Consequently, PHFATTN provides a scalable, fault‑tolerant quantum computing substrate where logical gates are executed deterministically by exploiting the E8 lattice's geometric symmetry and phase‑locked spectral dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 7, 20260 citations

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