Related papers: Shortest Route to Non-Abelian Topological Order on…
Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of…
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.…
In this Letter, we construct a set of order parameters for non-Abelian gauge theories which probe directly the unbroken group and are free of the deficiencies caused by quantum fluctuations and gauge fixing which have plagued all previous…
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…
Long-range entanglement--the backbone of topologically ordered states--cannot be created in finite time using local unitary circuits, or equivalently, adiabatic state preparation. Recently it has come to light that single-site measurements…
The topological order is equivalent to the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order through…
Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing…
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…
In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states have attracted much attention recently. However, due to the operational difficulties in solid-state…
The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical…
We propose an approach to measure the quantum phase of an electron in a non-Abelian system using the algorithm of Quantum Phase Estimation (QPE). The discrete-path systems were previously studied in the context of square or rectangular…
Owing to subtle issues concerning quantum fluctuations and gauge fixing, a formulation of a general procedure to specify the realization of non-Abelian gauge symmetry has evaded all earlier attempts. In this Letter, we discuss these…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
The non-Abelian geometric phases of the robust degenerate ground states were proposed as physically measurable defining properties of topological order in 1990. In this paper we discuss in detail such a quantitative characterization of…
A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an 'orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi- great circles. Since the dynamical…
We present protocols for preparing two-dimensional abelian and non-abelian topologically ordered states by employing finite depth unitary circuits composed of long-ranged, simultaneous, and mutually commuting two-qubit gates. Our protocols…
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 computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key…