Index Theory of One Dimensional Quantum Walks and Cellular Automata

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information” as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems — namely quantum walks and cellular automata — we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information” through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S 1, S 2 can be "pieced together”, in the sense that there is a system S which acts like S 1 in one region and like S 2 in some other region, if and only if S 1 and S 2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S 1 into S 2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map $${S \mapsto {\rm ind} S}$$ is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shift

Ancestral genome estimation reveals the history of ecological diversification in Agrobacterium

Horizontal gene transfer (HGT) is considered as a major source of innovation in bacteria, and as such is expected to drive adaptation to new ecological niches. However, among the many genes acquired through HGT along the diversification history of genomes, only a fraction may have actively contributed to sustained ecological adaptation. We used a phylogenetic approach accounting for the transfer of genes (or groups of genes) to estimate the history of genomes in Agrobacterium biovar 1, a diverse group of soil and plant-dwelling bacterial species. We identified clade-specific blocks of cotransferred genes encoding coherent biochemical pathways that may have contributed to the evolutionary success of key Agrobacterium clades. This pattern of gene coevolution rejects a neutral model of transfer, in which neighboring genes would be transferred independently of their function and rather suggests purifying selection on collectively coded acquired pathways. The acquisition of these synapomorphic blocks of cofunctioning genes probably drove the ecological diversification of Agrobacterium and defined features of ancestral ecological niches, which consistently hint at a strong selective role of host plant rhizospheres

Efficient and feasible state tomography of quantum many-body systems

We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for measuring a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary 2-designs, i.e., certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established techniques like optical super-lattices, laser speckles, and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. Combining our approach with tensor network methods - in particular the theory of matrix-product states - we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing in principle to perform tomography on large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing that no single-site addressing is needed at any stage of the scheme when implemented in optical lattice system

Index theory of one dimensional quantum walks and cellular automata

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information" as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems - namely quantum walks and cellular automata - we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information" through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S_1, S_2 can be pieced together, in the sense that there is a system S which locally acts like S_1 in one region and like S_2 in some other region, if and only if S_1 and S_2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S_1 into S_2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map S -> ind S is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.Comment: 38 pages. v2: added examples, terminology clarifie

Fate of CMY-2-encoding plasmids introduced into the human fecal microbiota by exogenous Escherichia coli

The gut is a hot spot for transfer of antibiotic resistance genes from ingested exogenous bacteria to the indigenous microbiota. The objective of this study was to determine the fate of two nearly identical blaCMY-2-harboring plasmids introduced into the human fecal microbiota by two Escherichia coli strains isolated from human and poultry meat, respectively. The chromosome and the CMY-2-encoding plasmid of both strains were labeled with distinct fluorescent markers (mCherry and GFP), allowing Fluorescence Activated Cell Sorting (FACS)-based tracking of the strain and the resident bacteria that have acquired its plasmid. Each strain was introduced into an established in vitro gut model (CoMiniGut) inoculated with individual feces from ten healthy volunteers. Fecal samples collected 2, 6 and 24 h after strain inoculation were analyzed by FACS and plate counts. Although the human strain survived better than the poultry meat strain, both strains transferred their plasmids to the fecal microbiota at concentrations as low as 102 CFU/mL. Strain survival and plasmid transfer varied significantly depending on inoculum concentration and individual fecal microbiota. Identification of transconjugants by 16S rRNA gene sequencing and MALDI-TOF mass spectrometry revealed that the plasmids were predominantly acquired by Enterobacteriaceae such as E. coli and Hafnia alvei. Our experimental data demonstrate that exogenous E. coli of human or animal origin can readily transfer CMY-2-encoding IncI1 plasmids to the human fecal microbiota. Low amounts of exogenous strain are sufficient to ensure plasmid transfer if the strain is able to survive the gastric environment

Surface flux evolution constraints for flux transport dynamos

The surface flux transport (SFT) model of solar magnetic fields involves empirically well-constrained velocity and magnetic fields. The basic evolution of the Sun's large-scale surface magnetic field is well described by this model. The azimuthally averaged evolution of the SFT model can be compared to the surface evolution of the flux transport dynamo (FTD), and the evolution of the SFT model can be used to constrain several near-surface properties of the FTD model. We compared the results of the FTD model with different upper boundary conditions and diffusivity profiles against the results of the SFT model. Among the ingredients of the FTD model, downward pumping of magnetic flux, related to a positive diffusivity gradient, has a significant effect in slowing down the diffusive radial transport of magnetic flux through the solar surface. Provided the pumping was strong enough to give rise to a downflow of a magnetic Reynolds number of 5 in the near-surface boundary layer, the FTD using a vertical boundary condition matches the SFT model based on the average velocities above the boundary layer. The FTD model with a potential field were unable to match the SFT results.Comment: Accepted for A&

Small-scale solar magnetic fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.Comment: 43 pages, 18 figure