Related papers: Topological quantum computation assisted by phase …
We study the construction of both universal quantum computation and multi-partite entangled states in the topological diagrammatical approach to quantum teleportation. Our results show that the teleportation-based quantum circuit model…
A prominent example of a topologically ordered system is Kitaev's quantum double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from the point of…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
Models for topological quantum computation are based on braiding and fusing anyons (quasiparticles of fractional statistics) in (2+1)-D. The anyons that can exist in a physical theory are determined by the symmetry group of the Hamiltonian.…
Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, a control quantum system can coherently determine the order in which a target quantum system…
The moduli space of gapped Hamiltonians that are in the same topological phase is an intrinsic object that is associated to the topological order. The topology of these moduli spaces is used recently in the construction of Floquet codes. We…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We propose and analyse an efficient scheme for simulating higher-order topological phases of matter in two dimensional (2D) spin-phononic crystal networks. We show that, through a specially designed periodic driving, one can selectively…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the…
Floquet engineering of topological phase transitions driven by a high-frequency time-periodic field is a promising approach to realizing new topological phases of matter distinct from static states. Here, we theoretically investigate…
The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…
Quantum simulator with the ability to harness the dynamics of complex quantum systems has emerged as a promising platform for probing exotic topological phases. Since the flexibility offered by various controllable quantum systems has…
We presented the topological current of Ehrenfest definition of phase transition. It is shown that different topology of the configuration space corresponds to different phase transition, it is marked by the Euler number of the interaction…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…
Non-Abelian topological insulators are characterized by matrix-valued, non-commuting topological charges with regard to more than one energy gap. Their descriptions go beyond the conventional topological band theory, in which an additive…
A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only…
Understanding quantum phase transitions in physical systems is fundamental to characterize their behavior at low temperatures. Achieving this requires both accessing good approximations to the ground state and identifying order parameters…