Saturday, October 3, 2009

Quantum simulation

In a quantum simulation, the evolution of a quantum many-body system is 'emulated' by mapping the Hamiltonian onto the one of a real system or by encoding in qubits [for a review see Buluta and Nori, Science 326, 108 (2009)]. This will be particularly important if the exponentially growing computational complexity does not allow for a simulation on a classical computer.
This will be easier to implement than systems for quantum computation, since smaller systems and lower accuracies would suffice, and decoherence could in some cases even be taken advantage of for the simulation of open systems.
There is still something that classical computational physicists and their computers could learn from the field of quantum computing/simulation: the development of classical algorithms for simulation based on ideas from quantum information science (see e.g. Chap. 5 in R. Orus' PhD thesis [link]).

Friday, July 31, 2009

Imaginary time projection method for construction of localized basis sets

In the preprint arXiv:0907.5053v1, the authors Zhou and Ceperley present an efficient method to construct a localized basis set for a Hubbard lattice model of bosonic atoms in a disordered potential at a given instance of disorder. This is achieved by a projection technique based on propagation in imaginary time, which is related to diffusion processes of the atoms.

Thursday, July 23, 2009

Apollo 11 code published online

Parts of the code running on Apollo 11's control system have been published on Google code, based on the transcription of scanned images of the assembler source code from the MIT Museum. The codes can be run on an open source Apollo guidance computer emulator.

Tuesday, July 21, 2009

FPGAs solve N=26 queens problem

While NQueens@Home is still working on it, the Queens@TUD project has solved the N=26 queens problem, that is, in how many different ways 26 queens can be placed on a chessboard without the possibility of capture among them. The solution is 22,317,699,616,364,044. Are local, "uncrowded" solutions faster after all? ;)

Saturday, July 18, 2009

Games motivating human computing power

Tasks like image recognition can generally not be reliably performed by computers yet, but for humans this is relatively easy. While I would say that the scope of computational physics essentially involves problems that are too complex to be solved by hand, there are problems where intuition will help finding a solution instead of barely relying on e.g. brute force computational-only approaches, i.e. the road from theory(thinking/modeling) to computational physics would be extended once more by cognitive power.

In the following I've listed three projects in the order I've come across them, each of them one step closer to the use of parallel human computing power in the field of computational condensed matter physics.

Read on

In this first video, Luis von Ahn illustrates how a large crowd can be motivated using "games with a purpose" to e.g. label images or to build up common-sense facts databases.

This video is about the game "Foldit", in which the score of a player is based on the optimality of a interactively folded protein.

In the following video, the spectral game (link; journal ref) is introduced.

It is intended as an educational game, but I guess a similar game could aim at predicting crystal structures by allowing the player to select a space group and to choose the sites of the elements of a given formula - the score would be based on how well e.g. powder diffraction patterns are reproduced (however, I have to admit that this wouldn't be a game I'd like to play). More fun could be the interactive construction of candidate structures by "mating" given starting cells (mixing slices etc.), in the spirit of genetic algorithm approaches to the crystal symmetry prediction problem.

Since "knowledge/intuition-based image processing" is something where games are very useful, it would be nice if "less visual" problems could be mapped onto kind of a 2D-image analysis problem.

Saturday, July 11, 2009

3D layered FQHE

Read on

Simulation of a 3D FQHE system. Suggested reading:

Fractional charges fly between planes
Burnell, Sondhi
Physics 2, 49 (2009)

Gapless layered three-dimensional fractional quantum Hall states
Levin, Fisher
Phys. Rev. B 79, 235315 (2009)

Bismuth in strong magnetic fields: Unconventional Zeeman coupling and correlation effects
Alicea, Balents
Phys. Rev. B 79, 241101(R) (2009)

Monday, June 29, 2009

What’s computational physics about?

Is it a subfield of theory? What about  - uhmm - “numerical experiments” (if there’s something like that)?

One could consider numerical simulation a third paradigm of science besides theory and experiment (see e.g. this link).
The term “numerical experiment”, however, would suggest a black box concept, i.e. you feed some input into the code and get numbers out, but don’t necessarily understand how and why it works and therefore not even if the output means anything.
So I would prefer the term “simulation” and make computational physics a part of theory and apply it to problems which are too complex to be solved by hand. Along this line scientific computing can aim at providing new “tools of discovery” of complex phenomena.

What do you think “scientific computing” is about and do you think it is important at all to decide which field it belongs to?

Thursday, June 25, 2009

Bandstructure code from 1972

Electronic bandstructure of cubic YZn calculated with an APW code from the early 70's.

Are there still source codes of other old bandstructure programs available?

See further details about how to compile and use the code on nowadays hardware below.

In 1972, Hoffstein, Ray, and Belakhovsky have published a symmetrized augmented planewave code (Comput. Phys. Commun. 4 361 (1972)), which I've used to calculate the data shown in the figure above. Neither source nor binary must be distributed. You need access to the Computer Physics Communications Program Library to get the source code (tip: search for the authors to find the archive).

The program was written in Fortran IV (≈ Fortran 66) and the file you download is a punch code conversion containing the command line for the compilation, the source code, what is fed to standard input...
To extract the Fortran code and the input data run:
zcat acmj_v1_0.gz | tail +10 | head -1224 >sapw.f
zcat acmj_v1_0.gz | tail +1308 | head -313 >>sapw.f
zcat acmj_v1_0.gz | tail +1622 | head -506 >inph

We've skipped a few lines of the source code, which back in the days served for the calculation of a float encoded in a four character string in a special (but simple) way. The replacement of this routine for other hardware was actually worth a second publication by de Hosson in 1975 ( ...

We'll take advantage of something else that was developed in 1972 - C - to implement this simple conversion:
/* conv.c */

double conv_(char *x)
double sign = 1., c = 0., d;
int i;

for(i=0, d=1000.; i<4; i++, d/=10.) {
switch(x[i]) {
case '+':
sign = 1.;
case '-':
sign = -1.;
case 'A':
c += sign * d * 0.86602540378;
case 'B':
c += sign * d * 0.5;
case 'C':
c += sign * d * 1.5;
case 32:
c += ((double) (x[i]-48)) * sign * d;

return c;
Phew, what a masterpiece ;)

Compile with:
gcc -O2 -c conv.c
gfortran -O2 -fdefault-real-8 -o sapw sapw.f conv.o

The following python script can be used to calculate the dispersion from Γ to R:
from os import system,popen

e = []
for i in range(9):

for s in (-2.0,-1.8,-1.5,-1.2,-1.0,-0.7,-0.5,-0.2,0.4,0.6,0.8):
for i in range(9):
k = float(i)/10.+0.1

system('cat inph >inp')
f = open('inp','a')
print >>f,' %g %g %g' % (k,k,k)
print >>f,' -4 3 1 1 1 R 15 BANDS\n %g 0.05 50' %s

p = popen("./sapw <inp | grep EIGENVA | awk '{print $3}'")
a = p.readline().strip()
if len(a)
e[i][a] = 1

for i in range(9):
k = float(i)/10.+0.1
q = e[i].keys()
for a in q:
print k, float(a)*2.0

Friday, June 19, 2009

You spin my subspace right round... - direct minimization in DFT for metallic systems

The article
Direct minimization technique for metals in density functional theory
Freysoldt, Boeck, Neugebauer
Phys. Rev. B 79, 241103(R) (2009)
describes a method for the direct minimization of the expansion coefficients of the Kohn-Sham orbitals in a density functional theory scheme with simultaneous and consistent updates of occupation numbers and subspace rotations.
This extension to previous approaches allowed the authors to perform fast direct-minimization-DFT calculations for metallic systems (the convergence of which depends sensitively on changes in the Kohn-Sham Fermi surface during the iterations).
Since the KS orbitals have to be orthonormalized, the asymptotic complexity, however, is O(N3), i.e. the same as for self-consistent, iterative diagonalization of the KS Hamiltonian or any other KS orbital-based approach.