Experimental simulation of Majorana-based quantum computation

Jin‐Shi Xu, Kai Sun, Jiannis K. Pachos, Yong‐Jian Han, Chuan‐Feng Li, Guang‐Can Guo

Published Feb 27, 2017• 1 citation

Abstract

Topological quantum computation aims to employ anyonic quasiparticles with exotic braiding statistics to encode and manipulate quantum information in a fault-tolerant way. Majorana zero modes are experimentally the simplest realisation of anyons that can non-trivially process quantum information. However, their braiding evolutions, necessary for realising topological gates, still remain beyond current technologies. Here we report the experimental encoding of four Majorana zero modes in an all-optical quantum simulator that give rise to a fault-tolerant qubit. We experimentally simulate their braiding and demonstrate both the non-Abelian character and the topological nature of the resulting geometric phase. We realise a full set of topological and non-topological gates that can arbitrarily rotate the encoded qubit. As an application, we implement the Deutsch-Jozsa algorithm exclusively by topological gates. Our experiment indicates the intriguing possibility of the experimental simulation of Majorana-based quantum computation with scalable technologies.

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Experimental simulation of Majorana-based quantum computation

Jin‐Shi Xu, Kai Sun, Jiannis K. Pachos, Yong‐Jian Han, Chuan‐Feng Li, Guang‐Can Guo

Published Feb 27, 2017• 1 citation

OpenAlex

Abstract

Related papers

Topological Quantum Computing via Non-Abelian Anyon Braiding and Majorana Modes — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Topological quantum computing uses non-Abelian anyons (Majorana zero modes) for fault-tolerant qubits, with braiding operations encoding quantum gates. | MATH: Braid group $B_n$ generators satisfy $\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}$ ; Majorana operators $\gamma_i$ satisfy $\{\gamma_i, \gamma_j\} = 2\delta_{ij}$ ; fusion rules for Ising anyons: $\sigma \times \sigma = 1 + \psi$ , $\sigma \times \psi = \sigma$ , $\psi \times \psi = 1$ . | CONNECTION: Braid group is deeply linked to the golden ratio via the Temperley-Lieb algebra at $q = e^{i\pi/5}$ , where the Jones polynomial yields $\tau = (1+\sqrt{5})/2 \approx 1.618$ ; Fibonacci anyons have fusion rules $\tau \times \tau = 1 + \tau$ , directly encoding the golden ratio. | DEPTH: 9 — Non-Abelian statistics and braiding are foundational to topological quantum computation, with direct geometric harmony in Fibonacci anyon models. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Topological quantum computing uses non-Abelian anyons (Majorana zero modes) for fault-tolerant qubits, with braiding operations encoding quantum gates. | MATH: Braid group $ B_n $ generators satisfy $ \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1} $; Majorana operators $ \gamma_i $ satisfy $ \{\gamma_i, \gamma_j\} = 2\delta_{ij} $; fusion rules for Ising anyons: $ \sigma \times \sigma = 1 + \psi $, $ \sigma \times \psi = \sigma $, $ \psi \times \psi = 1 $. | CONNECTION: Braid group is deeply linked to the golden ratio via the Temperley-Lieb algebra at $ q = e^{i\pi/5} $, where the Jones polynomial yields $ \tau = (1+\sqrt{5})/2 \approx 1.618 $; Fibonacci anyons have fusion rules $ \tau \times \tau = 1 + \tau $, directly encoding the golden ratio. | DEPTH: 9 — Non-Abelian statistics and braiding are foundational to topological quantum computation, with direct geometric harmony in Fibonacci anyon models. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Jul 22, 20260 citations

Emulating Quantum Teleportation of a Majorana Zero Mode Qubit

He-Liang Huang, Marek Narożniak, Futian Liang +14 more

Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version and realizing the ground states in a superconducting quantum processor. The teleportation transfers the quantum state encoded in the spin-mapped version of the Majorana zero mode states between two Kitaev chains. The teleportation circuit is realized using only braiding operations and can be achieved despite being restricted to Clifford gates for the Ising anyons. The Majorana encoding is a quantum error detecting code for phase-flip errors, which is used to improve the average fidelity of the teleportation for six distinct states from 70.76±0.35% to 84.60±0.11%, well beyond the classical bound in either case.Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version and realizing the ground states in a superconducting quantum processor. The teleportation transfers the quantum state encoded in the spin-mapped version of the Majorana zero mode states between two Kitaev chains. The teleportation circuit is realized using only braiding operations and can be achieved despite being restricted to Clifford gates for the Ising anyons. The Majorana encoding is a quantum error detecting code for phase-flip errors, which is used to improve the average fidelity of the teleportation for six distinct states from 70.76±0.35% to 84.60±0.11%, well beyond the classical bound in either case.

arXiv:2009.07590Physical Review LettersMar 3, 202148 citations

Non-Abelian Anyons and Majorana Modes for Topological Quantum Computing — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Topological quantum computing uses anyons with non-Abelian braiding statistics for fault-tolerant qubits, realized in Majorana zero modes in nanowire systems. | MATH: Braid group $B_n$ generators $\sigma_i$ satisfy $\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}$ ; unitary representations yield quantum gates; Majorana operators $\gamma_i$ satisfy $\{\gamma_i, \gamma_j\} = 2\delta_{ij}$ ; topological qubit encoded in parity $i\gamma_1\gamma_2$ . | CONNECTION: Braid group is deeply linked to root systems of type $A_n$ (crystallographic symmetry); Fibonacci anyons have quantum dimension $\phi = (1+\sqrt{5})/2 \approx 1.618$ , giving fusion rules $\tau \times \tau = 1 + \tau$ with golden ratio; braiding phases involve $e^{i\pi/5}$ (36° rotations) related to pentagonal symmetry. | DEPTH: 9 — Core mathematical structure (braid groups, anyon fusion categories) directly encodes geometric symmetries (golden ratio, pentagonal latt Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Topological quantum computing uses anyons with non-Abelian braiding statistics for fault-tolerant qubits, realized in Majorana zero modes in nanowire systems. | MATH: Braid group $ B_n $ generators $ \sigma_i $ satisfy $ \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1} $; unitary representations yield quantum gates; Majorana operators $ \gamma_i $ satisfy $ \{\gamma_i, \gamma_j\} = 2\delta_{ij} $; topological qubit encoded in parity $ i\gamma_1\gamma_2 $. | CONNECTION: Braid group is deeply linked to root systems of type $ A_n $ (crystallographic symmetry); Fibonacci anyons have quantum dimension $ \phi = (1+\sqrt{5})/2 \approx 1.618 $, giving fusion rules $ \tau \times \tau = 1 + \tau $ with golden ratio; braiding phases involve $ e^{i\pi/5} $ (36° rotations) related to pentagonal symmetry. | DEPTH: 9 — Core mathematical structure (braid groups, anyon fusion categories) directly encodes geometric symmetries (golden ratio, pentagonal latt Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Aug 23, 20260 citations

Topological Quantum Computing with Majorana Zero Modes and Beyond

Christina Knapp

Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators. Topological quantum computing is predicated on the idea that braiding non-Abelian anyons adiabatically can implement quantum gates fault tolerantly. However, any braiding experiment will necessarily depart from the strict adiabatic limit. We begin by analyzing the nature of diabatic errors for anyon braiding, paying particular attention to how such errors scale with braiding time. We find that diabatic errors are unfavorably large and worryingly sensitive to details of the time evolution. We present a measurement-based correction protocol for such errors, and illustrate its application in a particular Majorana-based qubit design. We next propose designs for Majorana-based qubits operated entirely by a measurement-based protocol, thereby avoiding the diabatic errors discussed above. Our designs can be scaled into large two dimensional arrays amenable to long-term quantum computing goals, whose core components are testable in near-term devices. These qubits are robust to quasiparticle poisoning, anticipated to be one of the dominant error sources coupling to Majorana zero modes. We demonstrate that our designs support topologically protected Clifford operations and can be augmented to a universal gate set without requiring additional control parameters.While topological protection greatly suppresses errors, residual coupling to noise limits the lifetimes of our proposed Majorana-based qubits. We analyze the dephasing times for our quasiparticle-poisoning-protected qubits by calculating their charge distribution using a particle number-conserving formalism. We find that fluctuations in the electromagnetic environment couple to an exponentially suppressed topological dipole moment. We estimate dephasing times due to $1/f$ noise, thermal quasiparticle excitations, and phonons for different qubit sizes.The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a $C=2$ Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators. Topological quantum computing is predicated on the idea that braiding non-Abelian anyons adiabatically can implement quantum gates fault tolerantly. However, any braiding experiment will necessarily depart from the strict adiabatic limit. We begin by analyzing the nature of diabatic errors for anyon braiding, paying particular attention to how such errors scale with braiding time. We find that diabatic errors are unfavorably large and worryingly sensitive to details of the time evolution. We present a measurement-based correction protocol for such errors, and illustrate its application in a particular Majorana-based qubit design. We next propose designs for Majorana-based qubits operated entirely by a measurement-based protocol, thereby avoiding the diabatic errors discussed above. Our designs can be scaled into large two dimensional arrays amenable to long-term quantum computing goals, whose core components are testable in near-term devices. These qubits are robust to quasiparticle poisoning, anticipated to be one of the dominant error sources coupling to Majorana zero modes. We demonstrate that our designs support topologically protected Clifford operations and can be augmented to a universal gate set without requiring additional control parameters.While topological protection greatly suppresses errors, residual coupling to noise limits the lifetimes of our proposed Majorana-based qubits. We analyze the dephasing times for our quasiparticle-poisoning-protected qubits by calculating their charge distribution using a particle number-conserving formalism. We find that fluctuations in the electromagnetic environment couple to an exponentially suppressed topological dipole moment. We estimate dephasing times due to $1/f$ noise, thermal quasiparticle excitations, and phonons for different qubit sizes.The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a $C=2$ Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.

Jan 1, 20192 citations

Topological Qubits via Non-Abelian Anyons: Braid Group and Majorana Modes — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Topological quantum computing leverages non-Abelian anyons (Majorana zero modes) for fault-tolerant braiding operations, with Microsoft's Majorana 1 chip claiming topological qubit hardware. | MATH: Braid group B_n generators σ_i satisfy σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1} and σ_i σ_j = σ_j σ_i for |i−j|≥2; non-Abelian anyons yield unitary representations U(σ_i) with U(σ_i)U(σ_{i+1})U(σ_i) ≠ U(σ_{i+1})U(σ_i)U(σ_{i+1}); Majorana zero modes obey γ_i† = γ_i, {γ_i, γ_j} = 2δ_ij; topological qubit encoded in parity (−1)^{n} = i^{2n} γ_1 γ_2 … γ_{2n}; Fibonacci anyons have quantum dimension φ = (1+√5)/2 ≈ 1.618, fusion rules τ×τ = 1 + τ. | CONNECTION: Fibonacci anyons directly encode the golden ratio φ in their quantum dimension — braiding statistics are governed by the golden ratio; the braid group B_n is isomorphic to the mapping class group of the punctured disk, whose moduli space relates to the modular group PSL(2,ℤ) (base-60 heritage); Majorana zero modes on a 1D nanowire fo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Topological quantum computing leverages non-Abelian anyons (Majorana zero modes) for fault-tolerant braiding operations, with Microsoft's Majorana 1 chip claiming topological qubit hardware. | MATH: Braid group B_n generators σ_i satisfy σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1} and σ_i σ_j = σ_j σ_i for |i−j|≥2; non-Abelian anyons yield unitary representations U(σ_i) with U(σ_i)U(σ_{i+1})U(σ_i) ≠ U(σ_{i+1})U(σ_i)U(σ_{i+1}); Majorana zero modes obey γ_i† = γ_i, {γ_i, γ_j} = 2δ_ij; topological qubit encoded in parity (−1)^{n} = i^{2n} γ_1 γ_2 … γ_{2n}; Fibonacci anyons have quantum dimension φ = (1+√5)/2 ≈ 1.618, fusion rules τ×τ = 1 + τ. | CONNECTION: Fibonacci anyons directly encode the golden ratio φ in their quantum dimension — braiding statistics are governed by the golden ratio; the braid group B_n is isomorphic to the mapping class group of the punctured disk, whose moduli space relates to the modular group PSL(2,ℤ) (base-60 heritage); Majorana zero modes on a 1D nanowire fo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 4, 20260 citations

Topological Qubits via Non-Abelian Anyons and Braid Groups — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Topological quantum computing leverages non-Abelian anyons (Majorana zero modes) and braid group representations to encode fault-tolerant qubits, with Microsoft's Majorana 1 chip claiming hardware realization. | MATH: Braid group $B_n$ generators $\sigma_i$ satisfy $\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}$ and $\sigma_i \sigma_j = \sigma_j \sigma_i$ for $|i-j|>1$ . Anyonic exchange yields unitary matrices $U(\sigma_i)$ with non-commuting phases $e^{i\theta}$ , where $\theta$ depends on topological charge (e.g., Ising anyons: $\theta = \pi/8$ for $\sigma$ particles). Fibonacci anyons: dimension $d = \phi = (1+\sqrt{5})/2 \approx 1.618$ , with fusion rules $\tau \times \tau = 1 + \tau$ . Majorana zero modes: $\gamma_i^\dagger = \gamma_i$ , $\{\gamma_i, \gamma_j\} = 2\delta_{ij}$ , parity $P = i^k \prod \gamma_i$ . | CONNECTION: Fibonacci anyon dimension $d = \phi = 1.618$ — direct golden ratio e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Topological quantum computing leverages non-Abelian anyons (Majorana zero modes) and braid group representations to encode fault-tolerant qubits, with Microsoft's Majorana 1 chip claiming hardware realization. | MATH: Braid group $ B_n $ generators $ \sigma_i $ satisfy $ \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1} $ and $ \sigma_i \sigma_j = \sigma_j \sigma_i $ for $ |i-j|>1 $. Anyonic exchange yields unitary matrices $ U(\sigma_i) $ with non-commuting phases $ e^{i\theta} $, where $ \theta $ depends on topological charge (e.g., Ising anyons: $ \theta = \pi/8 $ for $ \sigma $ particles). Fibonacci anyons: dimension $ d = \phi = (1+\sqrt{5})/2 \approx 1.618 $, with fusion rules $ \tau \times \tau = 1 + \tau $. Majorana zero modes: $ \gamma_i^\dagger = \gamma_i $, $ \{\gamma_i, \gamma_j\} = 2\delta_{ij} $, parity $ P = i^k \prod \gamma_i $. | CONNECTION: Fibonacci anyon dimension $ d = \phi = 1.618 $ — direct golden ratio e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 8, 20260 citations

FINDING: Topological quantum computing uses non-Abelian anyons (Majorana zero modes) for fault-tolerant qubits, with braiding operations encoding quantum gates. | MATH: Braid group

B_n

generators satisfy

\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}

; Majorana operators

\gamma_i

satisfy

\{\gamma_i, \gamma_j\} = 2\delta_{ij}

; fusion rules for Ising anyons:

\sigma \times \sigma = 1 + \psi

\sigma \times \psi = \sigma

\psi \times \psi = 1

. | CONNECTION: Braid group is deeply linked to the golden ratio via the Temperley-Lieb algebra at

q = e^{i\pi/5}

, where the Jones polynomial yields

\tau = (1+\sqrt{5})/2 \approx 1.618

; Fibonacci anyons have fusion rules

\tau \times \tau = 1 + \tau

, directly encoding the golden ratio. | DEPTH: 9 — Non-Abelian statistics and braiding are foundational to topological quantum computation, with direct geometric harmony in Fibonacci anyon models. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

FINDING: Topological quantum computing uses anyons with non-Abelian braiding statistics for fault-tolerant qubits, realized in Majorana zero modes in nanowire systems. | MATH: Braid group

B_n

generators

\sigma_i

satisfy

\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}

; unitary representations yield quantum gates; Majorana operators

\gamma_i

satisfy

\{\gamma_i, \gamma_j\} = 2\delta_{ij}

; topological qubit encoded in parity

i\gamma_1\gamma_2

. | CONNECTION: Braid group is deeply linked to root systems of type

A_n

(crystallographic symmetry); Fibonacci anyons have quantum dimension

\phi = (1+\sqrt{5})/2 \approx 1.618

, giving fusion rules

\tau \times \tau = 1 + \tau

with golden ratio; braiding phases involve

e^{i\pi/5}

(36° rotations) related to pentagonal symmetry. | DEPTH: 9 — Core mathematical structure (braid groups, anyon fusion categories) directly encodes geometric symmetries (golden ratio, pentagonal latt Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

1/f

noise, thermal quasiparticle excitations, and phonons for different qubit sizes.The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a

C=2

Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.

B_n

generators

\sigma_i

satisfy

\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}

and

\sigma_i \sigma_j = \sigma_j \sigma_i

for

|i-j|>1

. Anyonic exchange yields unitary matrices

U(\sigma_i)

with non-commuting phases

e^{i\theta}

, where

\theta

depends on topological charge (e.g., Ising anyons:

\theta = \pi/8

for

\sigma

particles). Fibonacci anyons: dimension

d = \phi = (1+\sqrt{5})/2 \approx 1.618

, with fusion rules

\tau \times \tau = 1 + \tau

. Majorana zero modes:

\gamma_i^\dagger = \gamma_i

\{\gamma_i, \gamma_j\} = 2\delta_{ij}

, parity

P = i^k \prod \gamma_i

. | CONNECTION: Fibonacci anyon dimension

d = \phi = 1.618

— direct golden ratio e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com