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Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…

Quantum Physics · Physics 2025-08-15 Themba Hodge , Philipp Frey , Stephan Rachel

We study systematically numerical method into constructing a universal quantum gate set for topological quantum computation (TQC) using SU(2)k anyon models. The F-matrices and R-symbol were computed through the q-deformed representation…

Quantum Physics · Physics 2025-11-18 Jiangwei Long , Yizhi Li , Jianxin Zhong , Lijun Meng

We introduce a pentagon equation solver, available as part of SageMath, and use it to construct braid group representations associated to certain anyon systems. We recall the category-theoretic framework for topological quantum computation…

Quantum Algebra · Mathematics 2022-12-05 Willie Aboumrad

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial statistical transformations as one excitation is moved (braided) around another. Topological…

Quantum Physics · Physics 2009-11-13 Chuanwei Zhang , V. W. Scarola , Sumanta Tewari , S. Das Sarma

The Fibonacci topological order is the prime candidate for the realization of universal topological quantum computation. We devise minimal quantum circuits to demonstrate the non-Abelian nature of the doubled Fibonacci topological order, as…

Quantum Physics · Physics 2024-08-05 Sary Bseiso , Joel Pommerening , Richard R. Allen , Steven H. Simon , Layla Hormozi

A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons…

Quantum Physics · Physics 2020-08-11 Guanyu Zhu , Ali Lavasani , Maissam Barkeshli

We investigate the measurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al. [Phys. Rev. Lett. 101, 010501 (2008)] where the braiding operation is shown to be equivalent to a series of topological charge…

Mesoscale and Nanoscale Physics · Physics 2017-01-03 Huaixiu Zheng , Arpit Dua , Liang Jiang

We discuss how to significantly reduce leakage errors in topological quantum computation by introducing an irrelevant error in phase, using the construction of a CNOT gate in the Fibonacci anyon model as a concrete example. To be specific,…

Mesoscale and Nanoscale Physics · Physics 2008-12-13 Haitan Xu , Xin Wan

Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two…

Quantum Physics · Physics 2018-02-06 Stephen Bigelow , Claire Levaillant

We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In particular, we show how this can be achieved using brane-net…

Quantum Physics · Physics 2008-11-26 H. Bombin , M. A. Martin-Delgado

The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of three Fibonacci anyons, $\{|1\rangle, |\tau\rangle\}$, and the…

Quantum Physics · Physics 2023-06-29 Vivek Kumar Singh , Akash Sinha , Pramod Padmanabhan , Indrajit Jana

In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well…

Quantum Physics · Physics 2013-02-14 Ross B. McDonald , Helmut G. Katzgraber

We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by…

Quantum Physics · Physics 2025-11-13 Pavel Rytir , Phillip C. Burke , Christos Aravanis , Jiri Vala , Jakub Marecek

Quantum gates in topological quantum computation are performed by braiding non-Abelian anyons. These braiding processes can presumably be performed with very low error rates. However, to make a topological quantum computation architecture…

Quantum Physics · Physics 2016-04-22 Adrian Hutter , James R. Wootton

A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…

General Mathematics · Mathematics 2018-10-09 Juan Ospina

Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing…

Strongly Correlated Electrons · Physics 2017-03-01 Keren Li , Yidun Wan , Ling-Yan Hung , Tian Lan , Guilu Long , Dawei Lu , Bei Zeng , Raymond Laflamme

The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how…

High Energy Physics - Theory · Physics 2026-05-06 Sergey Mironov , Andrey Morozov

In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…

Quantum Physics · Physics 2009-11-11 N. E. Bonesteel , Layla Hormozi , Georgios Zikos , Steven H. Simon

Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The non-semisimple theory…

Quantum Physics · Physics 2026-04-23 Filippo Iulianelli , Sung Kim , Joshua Sussan , Aaron D. Lauda

We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the…

Quantum Physics · Physics 2009-09-21 Parsa Bonderson , Michael Freedman , Chetan Nayak