On the Complexity of Random Quantum Computations and the Jones Polynomial

There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical complexity of approximately simulating random quantum computations. We prove that random quantum computations cannot be classically simulated up to a constant total variation distance, under the assumption that (1) the Polynomial Hierarchy does not collapse and (2) the average-case complexity of relative-error approximations of the Jones polynomial matches the worst-case complexity over a constant fraction of random links. Our results provide a straightforward relationship between the approximation of Jones polynomials and the complexity of random quantum computations.Comment: 8 pages, 4 figure

Renormalization Group Evolution in the type I + II seesaw model

We carefully analyze the renormalization group equations in the type I + II seesaw scenario in the extended standard model (SM) and minimal supersymmetric standard model (MSSM). Furthermore, we present analytic formulae of the mixing angles and phases and discuss the RG effect on the different mixing parameters in the type II seesaw scenario. The renormalization group equations of the angles have a contribution which is proportional to the mass squared difference for a hierarchical spectrum. This is in contrast to the inverse proportionality to the mass squared difference in the effective field theory case.Comment: 13 pages, 4 figures; corrected error due to wrong superfield normalization in RG equations (24-28,C1-4) as well as error in RG equations of mixing parameters (38,43); RG equations of mixing angles depend on Majorana phase

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. Furthermore, we prove that for this class of Ising models the partition function does not vanish. Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing the leading coefficients of graph polynomials on bounded degree graphs. Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum circuits.Comment: 12 pages, 0 figures, published versio

Gauged Discrete Symmetries and Proton Stability

We discuss the results of a search for anomaly free Abelian Z_N discrete symmetries that lead to automatic R-parity conservation and prevents dangerous higher-dimensional proton decay operators in simple extensions of the minimal supersymmetric extension of the standard model (MSSM) based on the left-right symmetric group, the Pati-Salam group and SO(10). We require that the superpotential for the models have enough structures to be able to give correct symmetry breaking to MSSM and potentially realistic fermion masses. We find viable models in each of the extensions and for all the cases, anomaly freedom of the discrete symmetry restricts the number of generations.Comment: 8 pages, 2 figures; v2 : typos fixed, references adde

Lean Processes without Compromising Controls

In today’s economic environment, governments feel the pressure to operate more efficiently, and many are therefore considering the gradual and continuous process improvement that Lean provides. Lean begins by examining a process from beginning to end, without departmental barriers; identifying the parts of the process that are inefficient; making a case for Lean improvements; and improving the process by reducing activities and waste that don’t add value to the consumer of the process

The Mass-Radius Relation Of Young Stars. I. Usco 5, An M4.5 Eclipsing Binary In Upper Scorpius Observed By K2

We present the discovery that UScoCTIO 5, a known spectroscopic binary in the Upper Scorpius star-forming region (P = 34 days, M-tot sin(i) = 0.64M(circle dot)), is an eclipsing system with both primary and secondary eclipses apparent in K2 light curves obtained during Campaign 2. We have simultaneously fit the eclipse profiles from the K2 light curves and the existing RV data to demonstrate that UScoCTIO 5 consists of a pair of nearly identical M4.5 stars with M-A = 0.329 +/- 0.002 M-circle dot, R-A = 0.834 +/- 0.006 R-circle dot, M-B = 0.317 +/- 0.002 M-circle dot, and R-B = 0.810 +/- 0.006 R-circle dot. The radii are broadly consistent with pre-main-sequence ages predicted by stellar evolutionary models, but none agree to within the uncertainties. All models predict systematically incorrect masses at the 25%-50% level for the HR diagram position of these mid-M dwarfs, suggesting significant modifications to mass-dependent outcomes of star and planet formation. The form of the discrepancy for most model sets is not that they predict luminosities that are too low, but rather that they predict temperatures that are too high, suggesting that the models do not fully encompass the physics of energy transport (via convection and/or missing opacities) and/or a miscalibration of the SpT-T-eff scale. The simplest modification to the models (changing T-eff to match observations) would yield an older age for this system, in line with the recently proposed older age of Upper Scorpius (tau similar to 11 Myr).NASA Science Mission directorateW. M. Keck FoundationAstronom

M–M Bond-Stretching Energy Landscapes for M_2(dimen)_(4)^(2+) (M = Rh, Ir; dimen = 1,8-Diisocyanomenthane) Complexes

Isomers of Ir_2(dimen)_(4)^(2+) (dimen = 1,8-diisocyanomenthane) exhibit different Ir–Ir bond distances in a 2:1 MTHF/EtCN solution (MTHF = 2-methyltetrahydrofuran). Variable-temperature absorption data suggest that the isomer with the shorter Ir–Ir distance is favored at room temperature [K = ~8; ΔH° = −0.8 kcal/mol; ΔS° = 1.44 cal mol^(–1) K^(–1)]. We report calculations that shed light on M_2(dimen)_(4)^(2+) (M = Rh, Ir) structural differences: (1) metal–metal interaction favors short distances; (2) ligand deformational-strain energy favors long distances; (3) out-of-plane (A_(2u)) distortion promotes twisting of the ligand backbone at short metal–metal separations. Calculated potential-energy surfaces reveal a double minimum for Ir_2(dimen)_(4)^(2+) (4.1 Å Ir–Ir with 0° twist angle and ~3.6 Å Ir–Ir with ±12° twist angle) but not for the rhodium analogue (4.5 Å Rh–Rh with no twisting). Because both the ligand strain and A_(2u) distortional energy are virtually identical for the two complexes, the strength of the metal–metal interaction is the determining factor. On the basis of the magnitude of this interaction, we obtain the following results: (1) a single-minimum (along the Ir–Ir coordinate), harmonic potential-energy surface for the triplet electronic excited state of Ir_2(dimen)_(4)^(2+) (R_(e,Ir–Ir) = 2.87 Å; F_(Ir–Ir) = 0.99 mdyn Å^(–1)); (2) a single-minimum, anharmonic surface for the ground state of Rh_2(dimen)_(4)^(2+) (R_(e,Rh–Rh) = 3.23 Å; F_(Rh–Rh) = 0.09 mdyn Å^(–1)); (3) a double-minimum (along the Ir–Ir coordinate) surface for the ground state of Ir_2(dimen)_(4)^(2+) (R_(e,Ir–Ir) = 3.23 Å; F_(Ir–Ir) = 0.16 mdyn Å^(–1))