Prethermal Strong Zero Modes and Topological Qubits

We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This non-equilibrium dynamical phenomenon is a form of prethermalization, and occurs because of obstructions to the equilibriation of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a non-perturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes, and on trapped ion chains.Comment: 20 pages. v2: reorganized and added overview sectio

Long coherence times for edge spins

We show that in certain one-dimensional spin chains with open boundary conditions, the edge spins retain memory of their initial state for very long times. The long coherence times do not require disorder, only an ordered phase. In the integrable Ising and XYZ chains, the presence of a strong zero mode means the coherence time is infinite, even at infinite temperature. When Ising is perturbed by interactions breaking the integrability, the coherence time remains exponentially long in the perturbing couplings. We show that this is a consequence of an edge "almost" strong zero mode that almost commutes with the Hamiltonian. We compute this operator explicitly, allowing us to estimate accurately the plateau value of edge spin autocorrelator.Comment: 13 pages, 13 figures; references adde

Through Education & Economic Development

I. Securing Full Share In the Economic Bounty II. Building Momentum Towards Success III. HBCUs as Catalysts For Entrepreneurship IV. The Government As a Collaborato

Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries

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 of out-of-equilibrium classifications that extend the ten-fold way and systems with additional crystalline symmetries to periodically driven systems, we explore the anomalous topological zero modes that arise in $H_F$ from the coexistence of a dynamical space-time symmetry $M$ and antisymmetry $A$ of $G$, and classify them using a frequency-domain formulation. Moreover, we provide an interpretation of the resulting Floquet topological phases using a frequency lattice with a decoration represented by color degrees of freedom on the lattice vertices. These colors correspond to the coefficient $N$ of the group extension $\tilde{G}$ of $G$ along the frequency lattice, given by $N=Z\rtimes H^1[A,M]$. The distinct topological classifications that arise at different energy gaps in its quasi-energy spectrum are described by the torsion product of the cohomology group $H^{2}[G,N]$ classifying the group extension.Comment: 4 pages + supplementary materia

Exercise intervention in people with cancer undergoing adjuvant cancer treatment following surgery: a systematic review

BackgroundRemaining physically active during and after cancer treatment is known to improve associated adverse effects, improve overall survival and reduce the probability of relapse. This systematic review addresses the question: is an exercise training programme beneficial in people with cancer undergoing adjuvant cancer treatment following surgery.MethodsA systematic database search of Embase, Ovid, Medline without Revisions, SPORTDiscus, Web of Science, Cochrane Library and ClinicalTrials.gov for any randomised controlled trials (RCT) or non-RCT addressing the effect of an exercise training programme in those having adjuvant cancer treatment following surgery was conducted.ResultsThe database search yielded 6489 candidate abstracts of which 94 references included the required terms. A total of 17 articles were included in this review. Exercise training is safe and feasible in the adjuvant setting and furthermore may improve measures of physical fitness and health related quality of life (HRQoL).ConclusionThis is the first systematic review on exercise training interventions in people with cancer undergoing adjuvant cancer treatment following surgery. Due to the lack of adequately powered RCTs in this area, it remains unclear whether exercise training in this context improves clinical outcomes other physical fitness and HRQoL. It remains unclear what is the optimal timing of initiation of an exercise programme and what are the best combinations of elements within an exercise training programme to optimise training efficacy. Furthermore, it is unclear if initiating such exercise programmes at cancer diagnosis may have a long-lasting effect on physically activity throughout the subsequent life course