Related papers: Topological Quantum Computation from the 3-dimensi…
We introduce a recoupling theory for virtual braided trees. This recoupling theory can be utilized to incorporate swap gates into anyonic models of quantum computation.
These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we…
In this paper, we explore topological quantum computation augmented by subphases and phase transitions. We commence by investigating the anyon tunneling map, denoted as $\varphi$, between subphases of the quantum double model…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from…
Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution of a subspace of quantum states, to encode logical gates. We identify a special class of subspaces, for which a sequence of rotations…
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to…
We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the computational power of topological quantum…
These lecture notes offer a pedagogical yet concise introduction to topological quantum computing. The material focuses on topological superconductors and Majorana qubits. It concludes with a discussion of more general braiding phenomena.…
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing…
Quantum computing is captured in the formalism of the monoidal subcategory of $\textbf{Vect}_{\mathbb C}$ generated by $\mathbb C^2$ -- in particular, quantum circuits are diagrams in $\textbf{Vect}_{\mathbb C}$ -- while topological quantum…
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…
The theory of topological quantum computation is underpinned by two important classes of models. One is based on non-abelian Chern-Simons theory, which yields the so-called $\rm{SU}(2)_k$ anyon models that often appear in the context of…
We first give a brief exposition of our recent realization of anyonic quantum states on single M5-brane probes in 11D super-gravity backgrounds, by non-perturbative quantization of the topological sector of the self-dual tensor field on the…
This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…
Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed…
A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a…
We show that the braid-group extension of the monodromy-based topological quantum computation scheme of Das Sarma et al. can be understood in terms of the universal R matrix for the Ising model giving similar results to those obtained by…
The classification and characterization of topological phases of matter is well understood for ground states of gapped Hamiltonians that are well isolated from the environment. However, decoherence due to interactions with the environment…
We describe how continuous-variable abelian anyons, created on the surface of a continuous-variable analogue of Kitaev's lattice model can be utilized for quantum computation. In particular, we derive protocols for the implementation of…