Related papers: Topological quantum color code model on infinite l…
We propose and study a generalization of Kitaev's $\mathbb Z_2$ toric code on a square lattice with an additional global $U(1)$ symmetry. Using Quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
We demonstrate that the chiral $\mathbb{Z}_p$ toric code -- the quintessential model of topological order -- hosts additional, emergent topological phases when perturbed: descendant fractional quantum Hall-like states, which we term…
A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a…
It is now widely recognized that the toric code is a pure gauge-theory model governed by a projective Hamiltonian with topological orders. In this work, we extend the interplay between quantum information system and gauge-theory model from…
We study a translation invariant spin model in a three-dimensional regular lattice, called the cubic code model, in the presence of arbitrary extensive perturbations. Below a critical perturbation strength, we show that most states with…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce…
Motivated by the order fractionalization in Kitaev-Kondo model, we propose an exactly solvable spin-charge ladder model to study the order fractionalization with discrete symmetry. The spin-charge ladder is composed of a spin chain and a…
The coming quantum computation is forcing us to reexamine the cryptosystems people use. We are applying graph colorings of topological coding to modern information security and future cryptography against supercomputer and quantum computer…
We consider nontrivial topological phases in Floquet systems using unitary loops and stroboscopic evolutions under a static Floquet Hamiltonian $H_F$ in the presence of dynamical space-time symmetries $G$. While the latter has been subject…
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
We consider a theory of superselection sectors for infinite quantum spin systems, describing charges that can be approximately localized in cone-like regions. The primary examples we have in mind are the anyons (or charges) in topologically…
We review recent progress in Monte Carlo simulations of dense two-color QCD (QC$_2$D), focusing on the phase diagram, the equation of state, and the sound velocity in the low-temperature regime. In three-color QCD at finite density,…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
We present an algorithm to approximate partition functions of 3-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
We show that a superlattice potential can be employed to engineer topology in massive Dirac fermions in systems such as bilayer graphene, moir\'e graphene-boron nitride, and transition-metal dichalcogenide (TMD) monolayers and bilayers. We…
In this letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting non-local zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the…
Recently, in certain flat band lattice systems at commensurate fillings, fractional quantum Hall states have been found -- which have anyonic excitations. We study such systems away from commensuration, i.e. the ground state of an anyon gas…