Related papers: Braiding of non-Abelian anyons using pairwise inte…
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…
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…
Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically…
It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of…
A two-component fermion model with conventional two-body interactions was recently shown to have anyonic excitations. We here propose a scheme to physically implement this model by transforming each chain of two two-component fermions to…
We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyon. This knot lattice model bears abelian and non-abelian anyons as well as integral and fractional filling states that is similar to quantum Hall…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
Nonabelian topological orders host exotic anyons central to quantum computing, yet established realizations rely on case-by-case constructions that are often conceptually involved. In this work, we present a systematic construction of…
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In…
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…
Topological Quantum Computing has largely evolved towards a paradigm of manipulating edge localized Majorana within $p$-wave topological superconducting nanowires. To bridge the gap between physical qubit systems and quantum algorithms, we…
Topological quantum computation has been extensively studied due to its robustness against decoherence. A conventional way to realize it is by adiabatic operations---it requires relatively long time to accomplish so that the speed of…
We give a general proof for the existence and realizability of Clifford gates in the Ising topological quantum computer. We show that all quantum gates that can be implemented by braiding of Ising anyons are Clifford gates. We find that the…
Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $\mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states…
The prevalent approach to executing quantum algorithms on quantum computers is to break-down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate…
Recent advances in quantum dot platforms have opened new pathways for realizing Majorana zero modes (MZMs) and simulating topological quantum computation. Here we propose an experimentally feasible setup for implementing topological…
In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, the transition probabilities between adiabatic states are exponentially small. They are characterized by an…
Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated…
Non-Abelian anyons, a promising platform for fault-tolerant topological quantum computation, adhere to the charge super-selection rule (cSSR), which imposes restrictions on physically allowed states and operations. However, the…
Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally…