Related papers: Experimental Identification of Non-Abelian Topolog…
We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as…
Non-Abelian topological orders offer an intriguing path towards fault-tolerant quantum computation, where information can be encoded and manipulated in a topologically protected manner immune to arbitrary local noises and perturbations.…
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…
A topological order is a new quantum phase that is beyond Landau's symmetry-breaking paradigm. Its defining features include robust degenerate ground states, long-range entanglement and anyons. It was known that $R$- and $F$-matrices, which…
Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows…
It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local…
Topological quantum computers provide a fault-tolerant method for performing quantum computation. Topological quantum computers manipulate topological defects with exotic exchange statistics called anyons. The simplest anyon model for…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
The Fibonacci topological order is the prime candidate for the realization of universal topological quantum computation. We devise minimal quantum circuits to demonstrate the non-Abelian nature of the doubled Fibonacci topological order, as…
Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle…
The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much…
Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One…
Topologically ordered quantum matter exhibits intriguing long-range patterns of entanglement, which reveal themselves in subsystem entropies. However, measuring such entropies, which can be used to certify topological order, on large…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial statistical transformations as one excitation is moved (braided) around another. Topological…
The string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen provided ways to systematically label non-chiral topological orders in 2D. In those approaches, different topologically ordered…
Electrons are indivisible elementary particles, yet paradoxically a collection of them can act as a fraction of a single electron, exhibiting exotic and useful properties. One such collective excitation, known as a topological Majorana…
Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal…
Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum…
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum…