Related papers: Quantum Computing with $\mathbb{Z}_2$ Abelian anyo…
Topological phases in two dimensions support anyonic quasiparticle excitations that obey neither bosonic nor fermionic statistics. These anyon structures often carry global symmetries that relate distinct anyons with similar fusion and…
There are two schools of "measurement-only quantum computation". The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero modes (Ising anyons). Here we go beyond…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer…
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…
Topological quantum error correction based on the manipulation of the anyonic defects constitutes one of the most promising frameworks towards realizing fault-tolerant quantum devices. Hence, it is crucial to understand how these defects…
We present a scheme for universal topological quantum computation based on Clifford complete braiding and fusion of symmetry defects in the 3-Fermion anyon theory, supplemented with magic state injection. We formulate a fault-tolerant…
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…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
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…
While the realization of scalable quantum computation will arguably require topological stabilization and, with it, topological-hardware-aware quantum programming and topological-quantum circuit verification, the proper combination of these…
Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, when two of them are interchanged.…
Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In…
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…