Related papers: Ternary Logic Design in Topological Quantum Comput…
Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models.…
We introduce a pentagon equation solver, available as part of SageMath, and use it to construct braid group representations associated to certain anyon systems. We recall the category-theoretic framework for topological quantum computation…
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to…
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…
Among the list of major threats to quantum computation, quantum decoherence poses one of the largest because it generates losses to the environment within a computational system which cannot be recovered via error correction methods. These…
Anyons, quasiparticles living in two-dimensional spaces with exotic exchange statistics, can serve as the fundamental units for fault-tolerant quantum computation. However, experimentally demonstrating anyonic statistics is a challenge due…
We examine a class of operations for topological quantum computation based on fusing and measuring topological charges for systems with SU$(2)_4$ or $k=4$ Jones-Kauffman anyons. We show that such operations augment the braiding operations,…
These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we…
Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth…
We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with…
To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to…
Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution of a subspace of quantum states, to encode logical gates. We identify a special class of subspaces, for which a sequence of rotations…
The classification and characterization of topological phases of matter is well understood for ground states of gapped Hamiltonians that are well isolated from the environment. However, decoherence due to interactions with the environment…
A topological phase can undergo a phase transition driven by anyon condensation. A potential obstruction to such a mechanism could arise if there exists a symmetry between anyons that have non-trivial mutual statistics. Here we consider…
Anyon models are algebraic structures that model universal topological properties in topological phases of matter and can be regarded as mathematical characterization of topological order in two spacial dimensions. It is conjectured that…
Anyon systems are studied in connection with several interesting applications including high $T_C$ superconductivity and topological quantum computing. In this work we show that these systems can be realized starting from directed polymers…
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…
In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent…
The idea of topological quantum computation is to build powerful and robust quantum computers with certain macroscopic quantum states of matter called topologically ordered states. These systems have degenerate ground states that can be…