Related papers: Braid Matrices and Quantum Gates for Ising Anyons …
Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even…
Reliable manipulation of non-Abelian Ising anyons supported by Kitaev spin liquids may enable intrinsically fault-tolerant quantum computation. Here, we introduce a standalone scheme for both generating and detecting individual Ising anyons…
We develop a computation model for solving Boolean networks by implementing wires through quantum ground-mode computation and gates through identities following from angular momentum algebra and statistics. Gates are represented by…
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic…
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…
In a topological description of elementary matter proposed by Bilson-Thompson, the leptons and quarks of a single generation, together with the electroweak gauge bosons, are represented as elements of the framed braid group of three…
This is a tutorial review of methods to braid the world lines of non-Abelian anyons (Majorana zero-modes) in topological superconductors. That "Holy Grail" of topological quantum information processing has not yet been reached in the…
A defining feature of topologically ordered states of matter is the existence of locally indistinguishable states on spaces with non-trivial topology. These degenerate states form a representation of the mapping class group (MCG) of the…
Solutions to the Yang-Baxter equation - an important equation in mathematics and physics - and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum…
Topological quantum computation with Fibonacci anyons relies on the possibility of efficiently generating unitary transformations upon pseudoparticles braiding. The crucial fact that such set of braids has a dense image in the unitary…
We describe the hashing technique to obtain a fast approximation of a target quantum gate in the unitary group SU(2) represented by a product of the elements of a universal basis. The hashing exploits the structure of the icosahedral group…
Two-qubit gates are a fundamental constituent of a quantum computer and typically its most challenging operation. In a trapped-ion quantum computer, this is typically implemented with laser beams which are modulated in amplitude, frequency,…
We establish an identification between the spaces of $\alpha$-fusion trees in non-semisimple topological quantum computation (NSS TQC) and a family of homological representations of the braid group known as the Lawrence representations…
Anyons are exotic quasiparticles obeying fractional statistics,whose behavior can be emulated in artificially designed spin systems.Here we present an experimental emulation of creating anyonic excitations in a superconducting circuit that…
Finite Temperley-Lieb (TL) algebras are diagram-algebra quotients of (the group algebra of) the famous Artin's braid group $B_N$, while the affine TL algebras arise as diagram algebras from a generalized version of the braid group. We study…
Significant efforts are being directed towards developing a quantum annealer capable of solving combinatorial optimization problems. The challenges are Hamiltonian programming and large-scale implementations. Here we report quantum…
Schemes for topological quantum computation are usually based on the assumption that the system is initially prepared in a specific state. In practice, this state preparation is expected to be challenging as it involves non-topological…
The relationships between quantum entangled states and braid matrices have been well studied in recent years. However, most of the results are based on qubits. In this paper, We investigate the applications of 2-qutrit entanglement in the…
A global race towards developing a gate-based, universal quantum computer that one day promises to unlock the never before seen computational power has begun and the biggest challenge in achieving this goal arguably is the quality…
Three manifold topology is used to analyze the effect of anyonic interferometers in which the probe anyons' path along an arm crosses itself, leading to a "twisted" or braided space-time trajectory for the probe anyons. In the case of Ising…