Correlations in Disordered Solvable Tensor Network States

Solvable matrix product and projected entangled pair states evolved by dual and ternary-unitary quantum circuits have analytically accessible correlation functions. Here, we investigate the influence of disorder. Specifically, we compute the average behavior of a physically motivated two-point equal-time correlation function with respect to random disordered solvable tensor network states arising from the Haar measure on the unitary group. By employing the Weingarten calculus, we provide an exact analytical expression for the average of the $k$th moment of the correlation function. The complexity of the expression scales with $k!$ and is independent of the complexity of the underlying tensor network state. Our result implies that the correlation function vanishes on average, while its covariance is nonzero.Comment: 28 pages, 2 figures, comments welcom

Ternary unitary quantum lattice models and circuits in 2+12 + 1 dimensions

We extend the concept of dual unitary quantum gates to quantum lattice models in $2 + 1$ dimensions, by introducing and studying ternary unitary four-particle gates, which are unitary in time and both spatial dimensions. When used as building blocks of lattice models with periodic boundary conditions in time and space (corresponding to infinite temperature states), dynamical correlation functions exhibit a light-ray structure. We also generalize solvable MPS to two spatial dimensions with cylindrical boundary conditions, by showing that the analogous solvable PEPS can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bulk ternary unitary gates cancel out. We delineate and implement a numerical algorithm for computing such correlations by contracting the remaining tensors.Comment: 16 pages, 6 figure

Differential upregulation of host cell protein kinases by the replication of α-, β- and γ-herpesviruses provides a signature of virus-specific signalling

Infections with human herpesviruses share several molecular characteristics, but the diversified medical outcomes are distinct to viral subfamilies and species. Notably, both clinical and molecular correlates of infection are a challenging field and distinct patterns of virus-host interaction have rarely been defined: this study therefore focuses on the search for virus-specific molecular indicators. As previous studies have demonstrated the impact of herpesvirus infections on changes in host signalling path- ways, we illustrate virus-modulated expression levels of individual cellular protein kinases. Current data reveal (i) alpha- and beta-, gamma-herpesvirus-specific patterns of kinase modulation as well as (ii) differential levels of up-/downregulated kinase expression and phosphorylation, which collectively suggest (iii) defined signalling patterns specific for the various viruses (VSS) that may prove useful for defining molecular indicators. Combined, the study confirms the correlation between herpesviral replication and modulation of signalling kinases, possibly exploitable for the in vitro characterization of viral infections