Related papers: Decoding non-Abelian topological quantum memories
The loss of qubits - the elementary carriers of quantum information - poses one of the fundamental obstacles towards large-scale and fault-tolerant quantum information processors. In this work, we experimentally demonstrate a complete…
We study symmetries and defects of a wide class of two dimensional Abelian topological phases characterized by Lie algebras. We formulate the symmetry group of all Abelian topological field theories. The symmetries relabel quasiparticles…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the Fractional Quantum Hall Effect state at Landau level filling fraction nu=5/2. Since the braid group representation…
Fractionalized quasiparticles - anyons - bear a special role in present-day physics. At the same time, they display properties of interest both foundational, with quantum numbers that transcend the spin-statistics laws, and applied,…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
Fault-tolerant quantum computing will require accurate estimates of the resource overhead, but standard metrics such as gate fidelity and diamond distance have been shown to be poor predictors of logical performance. We present a scalable…
Error operator bases for systems of any dimension are defined and natural generalizations of the bit/sign flip error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of…
Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study $t$--$J$ models of $SU(2)$ spin-1/2. Their anyonic counterparts can be built from non-Abelian…
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances…
Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
The simulation of non-Abelian anyon braiding is a critical step towards fault-tolerant quantum computation. We introduce a framework for this task based on a one-dimensional Quasicrystal Inflation Code (QIC). The code is defined by a local…
We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control. Our protocol uses continuous measurements and…
Adiabatic quantum computation (AQC) is known to possess some intrinsic robustness, though it is likely that some form of error correction will be necessary for large scale computations. Error handling routines developed for circuit-model…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
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…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…