Classification of the phases of 1D spin chains with commuting Hamiltonians

We consider the class of spin Hamiltonians on a 1D chain with periodic boundary conditions that are (i) translational invariant, (ii) commuting and (iii) scale invariant, where by the latter we mean that the ground state degeneracy is independent of the system size. We correspond a directed graph to a Hamiltonian of this form and show that the structure of its ground space can be read from the cycles of the graph. We show that the ground state degeneracy is the only parameter that distinguishes the phases of these Hamiltonians. Our main tool in this paper is the idea of Bravyi and Vyalyi (2005) in using the representation theory of finite dimensional C^*-algebras to study commuting Hamiltonians.Comment: 8 pages, improved readability, added exampl

The analysis of the effect of tax on profitability indices in listed companies of Tehran Stock Exchange

Profitability is considered as the most complicated feature for a company to be understood and evaluated. These ratios included in profitability are applied for evaluating business capabilities and making the wages in comparison with all cost during a specific period of time. In a more accurate way, the ratios indicate the profitability of a company, having calculated the total costs and tax on revenue, operational efficiency, company pricing policies, assets profitability and company’s shareholders. The approach applied in this research is descriptive-analytic. Using the data of 28 companies listed in Tehran Stock Exchange from 2004 to 2010 and using panel data approach, the tax effects over the paid profitability indices were studied in this paper. The results achieved from all estimation cases point out a negative significant effects on various profitability indices. It should be mentioned that in order to relate the taxes to the profitability indices, the costs and the debts of a corporation can be referred. Results of the study indicated that the debts ratio to asset and the type of the industry showed a negative effect on profitability and capital ratio to asset and the size of the company indicated positive significant effects on profitability index

The analysis of the effect of tax on profitability indices in listed companies of Tehran Stock Exchange

Profitability is considered as the most complicated feature for a company to be understood and evaluated. These ratios included in profitability are applied for evaluating business capabilities and making the wages in comparison with all cost during a specific period of time. In a more accurate way, the ratios indicate the profitability of a company, having calculated the total costs and tax on revenue, operational efficiency, company pricing policies, assets profitability and company’s shareholders. The approach applied in this research is descriptive-analytic. Using the data of 28 companies listed in Tehran Stock Exchange from 2004 to 2010 and using panel data approach, the tax effects over the paid profitability indices were studied in this paper. The results achieved from all estimation cases point out a negative significant effects on various profitability indices. It should be mentioned that in order to relate the taxes to the profitability indices, the costs and the debts of a corporation can be referred. Results of the study indicated that the debts ratio to asset and the type of the industry showed a negative effect on profitability and capital ratio to asset and the size of the company indicated positive significant effects on profitability index

Qudit versions of the qubit "pi-over-eight" gate

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, when it supplements the set of Clifford gates then universal quantum computation can be achieved. The "pi-over-eight" gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under conjugation). Here we derive explicit expressions for all qudit (d-level, where d is prime) versions of this gate and analyze the resulting group structure that is generated by these diagonal gates. This group structure differs depending on whether the dimensionality of the qudit is two, three or greater than three. We then discuss the geometrical relationship of these gates (and associated states) with respect to Clifford gates and stabilizer states. We present evidence that these gates are maximally robust to depolarizing and phase damping noise, in complete analogy with the qubit case. Motivated by this and other similarities we conjecture that these gates could be useful for the task of qudit magic-state distillation and, by extension, fault-tolerant quantum computing. Very recent, independent work by Campbell, Anwar and Browne confirms the correctness of this intuition, and we build upon their work to characterize noise regimes for which noisy implementations of these gates can (or provably cannot) supplement Clifford gates to enable universal quantum computation.Comment: Version 2 changed to reflect improved distillation routines in arXiv:1205.3104v2. Minor typos fixed. 12 Pages,2 Figures,3 Table

Excitonic Effects and Optical Spectra of Single-Walled Carbon Nanotubes

Many-electron effects often dramatically modify the properties of reduced dimensional systems. We report calculations, based on an many-electron Green's function approach, of electron-hole interaction effects on the optical spectra of small-diameter single-walled carbon nanotubes. Excitonic effects qualitatively alter the optical spectra of both semiconducting and metallic tubes. Excitons are bound by ~ 1 eV in the semiconducting (8,0) tube and by ~ 100 meV in the metallic (3,3) tube. These large many-electron effects explain the discrepancies between previous theories and experiments.Comment: 6 pages, 3 figures, 2 table

Local Quantum Measurement and No-Signaling Imply Quantum Correlations

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.Comment: Published version. 5 pages, 1 figure

Clifford Gates by Code Deformation

Topological subsystem color codes add to the advantages of topological codes an important feature: error tracking only involves measuring 2-local operators in a two dimensional setting. Unfortunately, known methods to compute with them were highly unpractical. We give a mechanism to implement all Clifford gates by code deformation in a planar setting. In particular, we use twist braiding and express its effects in terms of certain colored Majorana operators.Comment: Extended version with more detail

The value of a simple method to decrease diagnostic errors in Turner syndrome: a case report

Introduction: Turner syndrome is a genetic disorder in females and is the result of complete or partial loss of an X chromosome during fertilization. The missing X chromosome is originally either from the mother's ovum or the father's sperm cell. Approximately 45% of patients have the 45,X karyotype and the rest have other variants of Turner syndrome, which are either mosaicism patterns or structural abnormalities of the X chromosome. Here, we report a case of Turner syndrome that is the fifth case of Turner syndrome with balanced Robertsonian translocation of (13;14)(q10;q10), and the sixth case with 44,X chromosomes, reported in the literature thus far. Case presentation: A 10.3-year-old Persian girl was brought to our clinic by her parents, with the complaint of failure to thrive and short height. She had been examined and investigated by endocrinologists since the age of 4 years, but no definite diagnosis was made. At the time of presentation, she had been through three provocative growth hormone tests and had been on no medications for about a year. Her physical examination revealed mild retrognathia and micrognathia. Initially, she was started on somatropin treatment which, after 12 months, did not appropriately improve her height velocity. Therefore, a more thorough physical examination was performed, in which high arched palate and low posterior hairline were observed. There was also a difference between target height and patient height standard deviation scores. Karyotype study was requested, and Turner syndrome was confirmed. Conclusion: The diagnosis of this case was not straightforward, both because the somatic presentations were not obvious, and because the physicians had not looked for them when performing the physical examinations. This case report introduces a rare 44,X chromosome karyotype of Turner syndrome and highlights the value in using the difference between target height and patient height standard deviation scores as a simple and inexpensive tool for diagnosis of this syndrome

Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms

The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted to bipartite graphs. Regarding the upper bound, we show that for any graph of order n, its local minimum degree is at most 3n/8+o(n) and n/4+o(n) for bipartite graphs, improving the known n/2 upper bound. We also prove that the local minimum degree is smaller than half of the vertex cover number (up to a logarithmic term). The local minimum degree problem is NP-Complete and hard to approximate. We show that this problem, even when restricted to bipartite graphs, is in W[2] and FPT-equivalent to the EvenSet problem, which W[1]-hardness is a long standing open question. Finally, we show that the local minimum degree is computed by a O*(1.938^n)-algorithm, and a O*(1.466^n)-algorithm for the bipartite graphs