On tensor network representations of the (3+1)d toric code

We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different virtual symmetries generated by string-like and membrane-like operators, respectively. We discuss the topological properties of the model from the point of view of these virtual symmetries, emphasizing the differences between both representations. In particular, we argue that, depending on the representation, the phase diagram of boundary entanglement degrees of freedom is naturally associated with that of a (2+1)d Hamiltonian displaying either a global or a gauge $\mathbb Z_2$-symmetry

The computational difficulty of finding MPS ground states

We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians which are known to be Matrix Product States (MPS). To this end, we construct a class of 1D frustration free Hamiltonians with unique MPS ground states and a polynomial gap above, for which finding the ground state is at least as hard as factoring. By lifting the requirement of a unique ground state, we obtain a class for which finding the ground state solves an NP-complete problem. Therefore, for these Hamiltonians it is not even possible to certify that the ground state has been found. Our results thus imply that in order to prove convergence of variational methods over MPS, as the Density Matrix Renormalization Group, one has to put more requirements than just MPS ground states and a polynomial spectral gap.Comment: 5 pages. v2: accepted version, Journal-Ref adde

Entanglement spectrum and boundary theories with projected entangled-pair states

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models, like a deformed AKLT [1], an Ising-type [2], and Kitaev's toric code [3], both in finite ladders and infinite square lattices. In the latter case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.Comment: 13 pages, 14 figure

Symmetry Protected Topological Order in Open Quantum Systems

We systematically investigate the robustness of symmetry protected topological (SPT) order in open quantum systems by studying the evolution of string order parameters and other probes under noisy channels. We find that one-dimensional SPT order is robust against noisy couplings to the environment that satisfy a strong symmetry condition, while it is destabilized by noise that satisfies only a weak symmetry condition, which generalizes the notion of symmetry for closed systems. We also discuss "transmutation" of SPT phases into other SPT phases of equal or lesser complexity, under noisy channels that satisfy twisted versions of the strong symmetry condition

The computational complexity of PEPS

We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to solve PP problems, the latter two tasks are both proven to be #P-complete. We further show how PEPS can be used to approximate ground states of gapped Hamiltonians, and that creating them is easier than creating arbitrary PEPS. The main tool for our proofs is a duality between PEPS and postselection which allows to use existing results from quantum compexity.Comment: 5 pages, 1 figure. Published version, plus a few extra

Control Flow Analysis for BioAmbients

AbstractThis paper presents a static analysis for investigating properties of biological systems specified in BioAmbients. We exploit the control flow analysis to decode the bindings of variables induced by communications and to build a relation of the ambients that can interact with each other. We eventually apply our analysis to an example of gene regulation by positive feedback taken from the literature

Single copy/knock-in models of ALS SOD1 in C. elegans suggest loss and gain of function have different contributions to cholinergic and glutamatergic neurodegeneration

Mutations in Cu/Zn superoxide dismutase 1 (SOD1) lead to Amyotrophic Lateral Sclerosis (ALS), a neurodegenerative disease that disproportionately affects glutamatergic and cholinergic motor neurons. Previous work with SOD1 overexpression models supports a role for SOD1 toxic gain of function in ALS pathogenesis. However, the impact of SOD1 loss of function in ALS cannot be directly examined in overexpression models. In addition, overexpression may obscure the contribution of SOD1 loss of function in the degeneration of different neuronal populations. Here, we report the first single-copy, ALS knock-in models in C. elegans generated by transposon- or CRISPR/Cas9- mediated genome editing of the endogenous sod-1 gene. Introduction of ALS patient amino acid changes A4V, H71Y, L84V, G85R or G93A into the C. elegans sod-1 gene yielded single-copy/knock-in ALS SOD1 models. These differ from previously reported overexpression models in multiple assays. In single-copy/knock-in models, we observed differential impact of sod-1 ALS alleles on glutamatergic and cholinergic neurodegeneration. A4V, H71Y, G85R, and G93A animals showed increased SOD1 protein accumulation and oxidative stress induced degeneration, consistent with a toxic gain of function in cholinergic motor neurons. By contrast, H71Y, L84V, and G85R lead to glutamatergic neuron degeneration due to sod-1 loss of function after oxidative stress. However, dopaminergic and serotonergic neuronal populations were spared in single-copy ALS models, suggesting a neuronal-subtype specificity previously not reported in invertebrate ALS SOD1 models. Combined, these results suggest that knock-in models may reproduce the neurotransmitter-type specificity of ALS and that both SOD1 loss and gain of toxic function differentially contribute to ALS pathogenesis in different neuronal populations.Peer reviewe

Bypassing state initialisation in perfect state transfer protocols on spin-chains

Although a complete picture of the full evolution of complex quantum systems would certainly be the most desirable goal, for particular Quantum Information Processing schemes such an analysis is not necessary. When quantum correlations between only specific elements of a many-body system are required for the performance of a protocol, a more distinguished and specialised investigation is helpful. Here, we provide a striking example with the achievement of perfect state transfer in a spin chain without state initialisation, whose realisation has been shown to be possible in virtue of the correlations set between the first and last spin of the transmission-chain.Comment: 8 pages, 2 figures, RevTeX

Projection, Spatial Correlations, and Anisotropies in a Large and Complete Sample of Abell Clusters

An analysis of R >= 1 Abell clusters is presented for samples containing recent redshifts from the MX Northern Abell Cluster Survey. The newly obtained redshifts from the MX Survey as well as those from the ESO Nearby Abell Cluster Survey (ENACS) provide the necessary data for the largest magnitude-limited correlation analysis of rich clusters in the entire sky (excluding the galactic plane) to date. We find 19.4 <= r_0 <= 23.3 h^-1Mpc, -1.92 <= gamma <= -1.83 for four different subsets of Abell/ACO clusters, including a large sample (N=104) of cD clusters. We have used this dataset to look for line-of-sight anisotropies within the Abell/ACO catalogs. We show that the strong anisotropies present in previously studied Abell cluster datasets are not present in our R >= 1 samples. There are, however, indications of residual anisotropies which we show are the result of two elongated superclusters, Ursa Majoris and Corona Borealis, whose axes lie near the line-of-sight. After rotating these superclusters so that their semi-major axes are prependicular to the line-of-sight, we find no anisotropies as indicated by the correlation function. The amplitude and slope of the two-point correlation function remain the same before and after these rotations. We also remove a subset of R = 1 Abell/ACO clusters that show sizable foreground/background galaxy contamination and again find no change in the amplitude or slope of the correlation function. We conclude that the correlation length of R >= 1 Abell clusters is not artificially enhanced by line-of-sight anisotropies.Comment: 37 pages, 8 figures, AASTeX Accepted for publication in Ap