Related papers: 3-Fermion topological quantum computation
In recent years, fermionic topological phases of quantum matter has attracted a lot of attention. In a pioneer work by Gu, Wang and Wen, the concept of equivalence classes of fermionic local unitary(FLU) transformations was proposed to…
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.
We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…
We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the…
We describe the chiral Kondo chain model based on the symplectic Kondo effect and demonstrate that it has a quantum critical ground state populated by non-Abelian anyons. We show that the fusion channel of two arbitrary anyons can be…
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal…
Using electrostatic gates to control the electron positions, we present a new controlled-NOT gate based on quantum dots. The qubit states are chosen to be the spin states of an excess conductor electron in the quantum dot; and the main…
We review the general strategy of topologically protected quantum information processing based on non-Abelian anyons, in which quantum information is encoded into the fusion channels of pairs of anyons and in fusion paths for multi-anyon…
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…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
We summarize the key ingredients required for universal topological quantum computation using Majorana zero modes in networks of topological superconductor nanowires. Particular emphasis is placed on the use of both sparse and dense logical…
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances…
The optimal regularization of infinite-dimensional degrees of freedom is a central open problem in the tractable simulation of lattice gauge theories on quantum computers. Here, we consider regularizing the gauge field by replacing the…
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 construct the totally antisymmetric structure constants f^{ABCD} of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants f^{ABCD} can be used to write down a…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
We propose an experimental design for universal continuous-variable quantum computation that incorporates recent innovations in linear-optics-based continuous-variable cluster state generation and cubic-phase gate teleportation. The first…
We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and…