Related papers: Incoherent dynamics in the toric code subject to d…

Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Here, we show that decoherence can also give rise to new types of topological order. Specifically, we construct concrete…

Topological phases of matter are considered the bedrock of novel quantum materials as well as ideal candidates for quantum computers that possess robustness at the physical level. The robustness of the topological phase at finite…

Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…

Anyons in a topologically ordered phase can carry fractional quantum numbers with respect to the symmetry group of the considered system, one example being the fractional charge of the quasiparticles in the fractional quantum Hall effect.…

We use large scale simulations to study interacting particles in two dimensions in the presence of both an ac drive and quenched disorder. As a function of ac amplitude, there is a crossover from a low drive regime where the colloid…

Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…

Topological stabilizer codes, such as the toric and surface codes, are leading candidates for fault-tolerant quantum computation. While their decodability under stochastic noise has been extensively studied, the effects of coherent errors,…

Multiple experiments on active systems consider oriented active suspensions on substrates or in chambers confined along one direction. The theories of polar and apolar phases in such geometries were considered in A. Maitra et al, arXiv…

Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the…

We study the effect of strong disorder on topology and entanglement in quench dynamics. Although disorder-induced topological phases have been well studied in equilibrium, the disorder-induced topology in quench dynamics has not been…

We explore the possibility of passive error correction in the toric code model. We first show that even coherent dynamics, stemming from spin interactions or the coupling to an external magnetic field, lead to logical errors. We then argue…

We study the two-dimensional toric code Hamiltonian with effective long-range interactions between its anyonic excitations induced by coupling the toric code to external fields. It has been shown that such interactions allow to increase the…

The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by…

We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to…

We introduce families of classical stochastic dynamics in two and higher dimensions which stabilize order in the absence of any symmetry. Our dynamics are qualitatively distinct from Toom's rule, and have the unusual feature of being…

We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…

This paper investigates the dynamical properties of tokens in pre-trained Transformer models and explores their application to improving Transformers. To this end, we analyze the dynamical system governing the continuous-time limit of the…

Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly…

The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…

Physical platforms such as trapped ions suffer from coherent noise where errors manifest as rotations about a particular axis and can accumulate over time. We investigate passive mitigation through decoherence free subspaces, requiring the…