Physics World

Google and Microsoft find new quasiparticle

Philip Ball

Published Jul 1, 2023• 0 citations

Abstract

The existence of so-called non-Abelian anyons has been reported by four independent teams, but plenty of challenges remain before they can transform quantum computing. Philip Ball explains.

DOI: 10.1088/2058-7058/36/07/10

Related papers

Quantum Computation with Abelian Anyons

Seth Lloyd

arXiv:quant-ph/0004010Quantum Information ProcessingApr 1, 200281 citations

Quantum Field Theories, Topological Materials, and Topological Quantum Computing

Ilyas, Muhammad

A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-Abelian anyons. Majorana fermions in topological superconductors and quasiparticles in some quantum Hall states are non-Abelian anyons. Such topological phases of matter have a ground state degeneracy. The fusion of two or more non-Abelian anyons can result in a superposition of several anyons. The topological quantum gates are implemented by braiding and fusion of the non-Abelian anyons. The fault-tolerance is achieved through the topological degrees of freedom of anyons. Such degrees of freedom are non-local, hence inaccessible to the local perturbations. In this dissertation, we provide a comprehensive review of the fundamentals of logic design in topological quantum computing. The braid group and knot invariants in the skein theory are discussed. The physical insight behind the braiding is explained by the geometric phases and the gauge transformation. The mathematical models for the fusion and braiding are presented in terms of the category theory and the quantum deformation of the recoupling theory. The topological phases of matter are described by the topology of band structure. The wave function of quasiparticles in the quantum Hall effect and the theory of Majorana fermions in topological superconductors are also discussed. The dynamics of the charge-flux composites and their Hilbert space are expressed through the Chern-Simons theory and the two-dimensional topological quantum field theory. The Ising and Fibonacci anyonic models for binary gates are briefly given. Ternary logic gates are more compact than their binary counterparts and naturally arise in a type of anyonic model called the metaplectic anyons. We reduced the quantum cost of the existing ternary quantum arithmetic gates and proposed that these gates can be implemented with the metaplectic anyons.

arXiv:2208.09707Dec 15, 20211 citation

Constructing and Deconstructing Non-Abelian Anyons

Bel 'en Paredes

Bulletin of the American Physical SocietyMar 2, 20150 citations

Ternary logic design in topological quantum computing

Muhammad Ilyas, Shawn Xingshan Cui, Marek A. Perkowski

Abstract A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-abelian anyons. Majorana fermions in topological superconductors and quasiparticles in some quantum Hall states are non-abelian anyons. Such topological phases of matter have a ground state degeneracy. The fusion of two or more non-abelian anyons can result in a superposition of several anyons. The topological quantum gates are implemented by braiding and fusion of the non-abelian anyons. The fault-tolerance is achieved through the topological degrees of freedom of anyons. Such degrees of freedom are non-local, hence inaccessible to the local perturbations. In this paper, the Hilbert space for a topological qubit is discussed. The Ising and Fibonacci anyonic models for binary gates are briefly given. Ternary logic gates are more compact than their binary counterparts and naturally arise in a type of anyonic model called the metaplectic anyons. The mathematical model, for the fusion and braiding matrices of metaplectic anyons, is the quantum deformation of the recoupling theory. We proposed that the existing quantum ternary arithmetic gates can be realized by braiding and topological charge measurement of the metaplectic anyons.

arXiv:2204.01000Journal of Physics A Mathematical and TheoreticalJun 22, 20226 citations

Topological Qubits via Non-Abelian Anyons: Majorana Braiding and Microsoft's Majorana 1 — 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} (Yang–Baxter); Majorana operators γ_i obey {γ_i, γ_j} = 2δ_ij; topological qubit encoded in parity iγ_1γ_2 = ±1; non-Abelian anyon exchange yields unitary matrices U(σ_i) = exp(θ σ_i) with θ = π/4 for Ising anyons (Fibonacci anyons: θ = 2π/5). | CONNECTION: Braid group relations are the algebraic shadow of the Yang–Baxter equation — the same structure underlying 2D crystallographic root systems (A_n, B_n, D_n) and the golden ratio appears in Fibonacci anyons: quantum dimension φ = (1+√5)/2 ≈ 1.618, with fusion rules τ⊗τ = 1⊕τ giving dimension φ² = φ+1. | DEPTH: 8 --- **Detailed analysis:** 1. **Key mathematical insight:** The core discovery is that topological phases of matter host quasiparticles (anyon Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Aug 24, 20260 citations

Detecting 3d Non-Abelian Anyons via Adiabatic Cooling

Seiji J. Yamamoto, Michael Hartley Freedman, Kun Yang

Bulletin of the American Physical SocietyMar 21, 20110 citations