Simulation of many-qubit quantum computation with matrix product states

Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete problem. Errors inherent to truncations of the exact action of interacting gates are controlled by the size of the matrices in the representation. The property of finding the right solution for an instance and the expected value of the energy are found to be remarkably robust against these errors. As a symbolic example, we simulate the algorithm solving a 100-qubit hard instance, that is, finding the correct product state out of ~ 10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow growth of the average minimum time to solve hard instances with highly-truncated simulations of adiabatic quantum evolution.Comment: 5 pages, 4 figures, final versio

Customer Orientation in Family Businesses

The purpose of this article is to investigate customer orientation of service employees (COSE) in family businesses. This study elaborates on the perception and importance of COSE in family-owned companies. The paper also proposes new consequences of COSE in the context of family business. The research is based on a qualitative study comprised of 13 interviews conducted on senior managers in family firms. The results are analysed using NVivo 11. This investigation confirms the relevance of the COSE construct in family businesses and the role of family influence over it. New consequences are elicited, including differentiation, customer experience, and customer well-being. The results show that practitioners consider COSE as a key element for success. This study sheds light on how COSE can be applied in a family business in order to enhance customer experience. This study expands on the potential of COSE with the use of family businesses for the first time and introduces new consequences from the original model

A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta

We searched integrable 2D homogeneous polynomial potential with a polynomial first integral by using the so-called direct method of searching for first integrals. We proved that there exist no polynomial first integrals which are genuinely cubic or quartic in the momenta if the degree of homogeneous polynomial potentials is greater than 4.Comment: 22 pages, no figures, to appear in J. Phys. A: Math. Ge

Center of mass momentum dependence of short-range correlations with the coarse-grained Granada potential

The effect of the center of mass motion on the high-momentum distributions of correlated nucleon pairs is studied by solving the Bethe-Goldstone equation in nuclear matter with the Granada nucleon-nucleon potential. We show that this coarse-grained potential reduces the problem to an algebraic linear system of five (ten) equations for uncoupled (coupled) partial waves that can be easily solved. The corresponding relative wave functions of correlated pn, pp and nn pairs are computed for different values of their CM momentum. We find that the pn pairs dominate the high-momentum tail of the relative momentum distribution, and that this only depends marginally on center of mass momentum. Our results provide further justification and agreement for the factorization approximation commonly used in the literature. This approximation assumes that the momentum distribution of nucleon pairs can be factorized as the product of the center of mass momentum distribution and the relative momentum distribution.Comment: 27 pages, 12 figures, corrected the treatment of the coupled nucleon-nucleon partial waves, new authors adde

Evidence of ongoing radial migration in NGC 6754: Azimuthal variations of the gas properties

Understanding the nature of spiral structure in disk galaxies is one of the main, and still unsolved questions in galactic astronomy. However, theoretical works are proposing new testable predictions whose detection is becoming feasible with recent development in instrumentation. In particular, streaming motions along spiral arms are expected to induce azimuthal variations in the chemical composition of a galaxy at a given galactic radius. In this letter we analyse the gas content in NGC 6754 with VLT/MUSE data to characterise its 2D chemical composition and H$\alpha$ line-of-sight velocity distribution. We find that the trailing (leading) edge of the NGC 6754 spiral arms show signatures of tangentially-slower, radially-outward (tangentially-faster, radially-inward) streaming motions of metal-rich (poor) gas over a large range of radii. These results show direct evidence of gas radial migration for the first time. We compare our results with the gas behaviour in a $N$-body disk simulation showing spiral morphological features rotating with a similar speed as the gas at every radius, in good agreement with the observed trend. This indicates that the spiral arm features in NGC 6754 may be transient and rotate similarly as the gas does at a large range of radii.Comment: 8 pages, 4 figures, accepted for publication in ApJL 2016 September 2

Summability of the perturbative expansion for a zero-dimensional disordered spin model

We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method.Comment: LaTeX, 12 pages and 4 figure