Genetic braid optimization: A heuristic approach to compute quasiparticle braids

In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well as Leijnse and Flensberg [Phys. Rev. B 86, 104511 (2012)] recently provided schemes for computing quantum gates from quasiparticle braids. Mathematically, the problem of executing a gate becomes that of finding a product of the generators (matrices) in that set that approximates the gate best, up to an error. To date, efficient methods to compute these gates only strive to optimize for accuracy. We explore the possibility of using a generic approach applicable to a variety of braiding problems based on evolutionary (genetic) algorithms. The method efficiently finds optimal braids while allowing the user to optimize for the relative utilities of accuracy and/or length. Furthermore, when optimizing for error only, the method can quickly produce efficient braids.Comment: 6 pages 4 figure

Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils

Solution of 3-dimensional time-dependent viscous flows. Part 3: Application to turbulent and unsteady flows

A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed

Compiled data on the vascular aquatic plant program, 1975 - 1977

The performance of a single cell, facultative sewage lagoon was significantly improved with the introduction of vascular aquatic plants. Water hyacinth (Eichhornia crassipes) was the dominant plant from April to November; duckweed (Lemna spp.) and (Spirodela spp.) flourished from December to March. This 2 ha lagoon received approximately 475 cu m/day of untreated sewage and has a variable COD sub 5 loading rate of 22-30 kg/ha/day. During the first 14 months of operation with aquatic plants, the average influent BOD sub 5 was reduced by 95% from 110 mg/l to an average of 5 mg/l in the effluent. The average influent suspended solids were reduced by 90% from 97 mg/l to 10 mg/l in the effluent. Significant reductions in nitrogen and phosphorus were effected. The monthly kjeldahl nitrogen for influent and effluent averaged 12.0 and 3.4 mg/l, respectively, a reduction of 72%. The total phosphorus was reduced on an average of 56% from 3.7 mg/l influent to 1.6 mg/l effluent