Related papers: Topological quantum color code model on infinite l…
We present a three-dimensional cubic lattice spin model, anisotropic in the $\hat{z}$ direction, that exhibits fracton topological order. The latter is a novel type of topological order characterized by the presence of immobile pointlike…
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…
We delineate equilibrium phase structure and topological charge distribution of dense two-colour QCD at low temperature by using a lattice simulation with two-flavour Wilson fermions that has a chemical potential $\mu$ and a diquark source…
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported…
The topological susceptibility is an important quantity in QCD, which can be computed using lattice methods. However, at a fine lattice spacing, or when using high quality chirally symmetric quarks, algorithms which proceed in small update…
We derive the full spectrum of decorated Cayley trees that constitute tree analogs of selected two-dimensional Euclidean lattices; namely of the Lieb, the double Lieb, the kagome, and the star lattice. The common feature of these Euclidean…
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…
We show that interactions can drive a class of higher order topological superconductors (HOTSC) into symmetry enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting…
Lattice geometry continues providing exotic topological phases in condensed matter physics. Exciting recent examples are the higher-order topological phases, manifesting via localized lower-dimensional boundary states. Moreover, flat…
The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…
Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…
Locality-preserving logical operators in topological codes are naturally fault-tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure…
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy, and fidelity per lattice site by using the infinite matrix…
We introduce a class of 3D color codes, which we call stacked codes, together with a fault-tolerant transformation that will map logical qubits encoded in two-dimensional (2D) color codes into stacked codes and back. The stacked code allows…
Moir\'e superlattices provide a compelling platform for exploring exotic correlated physics. Electronic interference within these systems often results in flat bands with localized electrons, which are typically described by effective…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…
Topological subsystem color codes add to the advantages of topological codes an important feature: error tracking only involves measuring 2-local operators in a two dimensional setting. Unfortunately, known methods to compute with them were…