Related papers: Stability of topological purity under random local…
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum…
Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…
As a prototype model of topological quantum memory, two-dimensional toric code is genuinely immune to generic local static perturbations, but fragile at finite temperature and also after non-equilibrium time evolution at zero temperature.…
In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…
A safety verification task involves verifying a system against a desired safety property under certain assumptions about the environment. However, these environmental assumptions may occasionally be violated due to modeling errors or…
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…
More physics at the boundaries of a topological lattice remains to be explored for future applications of topological edge states. This work investigates the stability of topological edge states in the presence of a moving impurity. By…
We consider two-dimensional states of matter satisfying an uniform area law for entanglement. We show that the topological entanglement entropy is equal to the minimum relative entropy distance from the reduced state to the set of thermal…
We investigate the long-lived quantum coherence of two-level spontaneous emission models within structured environments. The population of the system under the asymptotic non-Markovian dynamics is linked to the spectral density of the…
This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…
Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…
We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
Despite its putative robustness, the realization of and control over topological quantum matter is an ongoing grand challenge. Looking forward, robust characterization protocols are needed to first certify topological substrates before they…