On measurement-based quantum computation with the toric code states

We study measurement-based quantum computation (MQC) using as quantum resource the planar code state on a two-dimensional square lattice (planar analogue of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer if at each step of MQC the sets of measured and unmeasured qubits correspond to connected subsets of the lattice.Comment: 9 pages, 5 figure

Subextensive singularity in the 2D ±J\pm J Ising spin glass

The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of $L$, in order to obtain the low temperature behavior of the model. For large finite $L$ there is a range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$. The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$ increases. Similar results are found for $p$ = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation $d \nu = 2 - \alpha$, even though $T_c = 0$. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented.Comment: 13 pages, 7 figures; final version, to appear in J. Stat. Phy

Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses

Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000x3000 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the Bieche et al. approach.Comment: 11 pages, 5 figures; shortened introduction, extended results; to appear in Physical Review E 7

Depinning transition of a directed polymer by a periodic potential: a d-dimensional solution

We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the polymer. We show that a bounded state can still arise even if, in average, the potential layer is not attractive and for diverging values of the potential on the repulsive sites. The phase transition is of second order.Comment: 11 Pages in LaTeX. Figures available from the authors. [email protected] (e-mail address

Graviton Spectra in String Cosmology

We propose to uncover the signature of a stringy era in the primordial Universe by searching for a prominent peak in the relic graviton spectrum. This feature, which in our specific model terminates an $\omega^3$ increase and initiates an $\omega^{-7}$ decrease, is induced during the so far overlooked bounce of the scale factor between the collapsing deflationary era (or pre-Big Bang) and the expanding inflationary era (or post-Big Bang). We evaluate both analytically and numerically the frequency and the intensity of the peak and we show that they may likely fall in the realm of the new generation of interferometric detectors. The existence of a peak is at variance with ordinarily monotonic (either increasing or decreasing) graviton spectra of canonical cosmologies; its detection would therefore offer strong support to string cosmology.Comment: 14 pages, RevTex source and 6 figures.p

Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants

We continue the discussion of the fermion models on graphs that started in the first paper of the series. Here we introduce a Graphical Gauge Model (GGM) and show that : (a) it can be stated as an average/sum of a determinant defined on the graph over $\mathbb{Z}_{2}$ (binary) gauge field; (b) it is equivalent to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the model allows an explicit expression in terms of a series over disjoint directed cycles, where each term is a product of local contributions along the cycle and the determinant of a matrix defined on the remainder of the graph (excluding the cycle). We also establish a relation between the MD model on the graph and the determinant series, discussed in the first paper, however, considered using simple non-Belief-Propagation choice of the gauge. We conclude with a discussion of possible analytic and algorithmic consequences of these results, as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte

Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors. [email protected] (e-mail address

Closed-Loop Manufacturing for Aerospace Industry: An Integrated PLM-MOM Solution to Support the Wing Box Assembly Process

The aim of this research is to provide an example of the importance that integrated Product Lifecycle Management (PLM) and Manufacturing Operation Management (MOM) systems have in realizing the Digital Manufacturing. The research first examines what the Digital Manufacturing involves and then identifies Digital Twin and the related Digital Thread as key elements. PLM and MOM solutions support the Digital Twin and the Digital Thread allowing the exchange of product-related information between the digital manufacturing model and the physical manufacturing execution. A Digital Twin of a wing box and its assembly process is created in PLM by building the bill of material and bill of process. Then it is shown how in MOM system the production phase is facilitated by managing production operations, advanced scheduling and supporting the execution of the processes and how the analysis of the manufacturing performance is possible. The result integrating these systems is to have the right information at the right place at the right time along with the related benefits in terms of costs, time and quality. The activity has been developed in Siemens Industry Software under the European Project AirGreen 2, an integrated research action of the REG IADP (Regional Innovative Aircraft Demonstration Platform) part of the Joint Technical Programme, the steering and coordination of LEONARDO Aircraft. The AirGreen 2 project is an Innovation Action funded by the Clean Sky 2 Joint Undertaking under the European Union\u2019s Horizon 2020 research and innovation programme, under Grant Agreement N\ub0807089 REG IADP)

Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect

A flux line in a Type-II superconductor with a single nonuniform columnar defect is studied by a perturbative diagrammatic expansion around an annealed approximation. The system undergoes a finite temperature depinning transition for the (rather unphysical) on-the-average repulsive columnar defect, provided that the fluctuations along the axis are sufficiently large to cause some portions of the column to become attractive. The perturbative expansion is convergent throughout the weak pinning regime and becomes exact as the depinning transition is approached, providing an exact determination of the depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st

Gauge Invariant Cutoff QED

A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that corresponding Ward identities are valid all along the renormalization group flow. The exact Renormalization Group flow equation corresponding to the effective action of a cutoff lambda phi^4 theory is also derived. Generalization to any gauge group is indicated.Comment: V1: 18 pages, 2 figures; V2: Discussions improved. Version accepted for publication in Physica Script