Ganesh Swami

Real life has been kicking my ass lately. My brain has been working over-time, so I’m taking some time off to relax. I’m fortunate to have a lot of friends with birthdays this week, so that helps. Anyways, here’s an update on what I’ve been upto…

Parabolic excitation

Working on a homework problem for my non-linear physics class has been a huge timesink. This week, we were asked to solve the general low viscosity Mathieu equation

for a parabolic excitation signal. My professor, Dr. Bechhoefer had published a paper to describe parametrically excited surface waves with delta and triangle excitation signals. We were asked to extend this. At the end, you get a complicated implicit equation for the threshold condition. I had to learn how to solve implicit equations numerically in Matlab (numerically because Maple couldn’t do it analytically.)

Geometry of Diffusion Tensors

As I’m working a lot with Diffusion Tensors, I wanted to get a better feel for the computations on them. I found this paper(pdf) by Dr. Joshi titled “Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors” really helpful. Ofcourse, I couldn’t understand some of the mathematical terms, so it’s more reading for me. I also realized that not all graduate students are on top of their game — they sometimes can mislead you. It’s better to mislead yourself than to be misled.

Geodesic Shooting

As part of my weekly reading, a friend and I are trying to understand this paper titled “Geodesic Shooting for Computational Anatomy.” Amidst all the complicated math, the basic idea they are trying to show is that flows on the deformation diffeomorphism conserve momentum. And because of this conservation law, you only need the velocity at t=0 to completely determine the flow. In the grand scheme of things, you do not and cannot average images just by averaging pixel/voxel intensities. This is because these images do not form a vector space and simple linear averaging does not respect the curved aspect of the space. The space of the velocity vectors form a vector space, and we can average those instead.

MRI scan

I also had my first MRI scan last week. I had to go all the way to the UBC hospital for that. A graduate friend of mine is doing some research on parameter optimization on the MR machine, but with about 400 controls you can tune, this is a very difficult problem. It was an interesting experience for me, though I slept through most of it. To take your mind off the heavy beating (and for claustrophobic people I guess,) they give you headphones. I wondered for a long time how electronic headphones worked in presence of a strong magnetic field (MR machines have a magnetic field strength of 1.5 to 3.0 tesla, in contrast to the earth’s field of 30 to 60 microteslas.) I’ll leave that question unanswered because it makes me feel too dumb.

That’s all for now. I’ll save the rest for later.

It’s about time I gave an update on my non-linear physics class.

We spent the last few weeks building a framework to analyze partial differential equations with non-linear terms. After the pedagogical material, we went on to our first real example: Faraday waves.

Faraday waves were first described in an appendix to a paper published in the Philosophical Transactions of the Royal Society of London in 1831. These are standing non-linear waves that are generated when an open container with fluid is subject to vertical oscillations. When the oscillations reach a certain threshold, we begin to see an instability on the surface of the fluid. Our professor did a demo for us with two fluids: canola and water. I had posted a video to Faraday waves with corn starch some time back.

A bunch of people had previously observed this phenomena, but Faraday was the one who had described that the oscillation frequency of the waves is half that of the driving frequency. I’ve read this original paper, and he goes into excruciating detail about his experiments. Surprisingly for a physics paper, there wasn’t a single equation.

I’d like to draw attention to the point that we get a frequency that is half that of the driving frequency. This is impossible in a linear system, whose transfer functions have complex exponentials as eigenfunctions. The mixing of the modes of the system is not arbitrary, in fact we determined them after a ton of math.

To finish off, I’m posting a video to Chladni patterns formed with different frequencies. For the sake of saving some brain cells, don’t read the comments on that video.

Pictures courtesy of Jerry Gollub.

As a British Columbian, D-wave’s story in the Economist makes me happy. This single story might have done more for the province than all the marketing the government has been trying to do. But today, I came across this note to the Economist by Umesh Vazirani:

Sir,

Your article “Orion’s belter” regarding D-Wave’s demonstration of a “practical quantum computer”, sets a new standard for sloppy science journalism. Most egregious is your assertion that quantum computers can solve NP-complete problems in “one shot” by exploring exponentially many solutions at once. This mistaken view was put to rest in the infancy of quantum computation over a decade ago when it was established that the axioms of quantum physics severely restrict the type of information accessible during a measurement. For unstructured search problems like the NP-complete problems this means that there is no exponential speed up but rather at most a quadratic speed up.

Your assertions about D-Wave are equally specious. A 16 qubit quantum computer has smaller processing power than a cell phone and hardly represents a practical breakthrough. Any claims about D-Wave’s accomplishments must therefore rest on their ability to increase the number of qubits by a couple of orders of magnitude while maintaining the fragile quantum states of the qubits. Unfortunately D-Wave, by their own admission, have not tested whether the qubits in their current implementation are in a coherent quantum state. So it is quite a stretch to assert that they have a working quantum computer let alone one that potentially scales. An even bleaker picture emerges when one more closely examines their algorithmic approach. Their claimed speedup over classical algorithms appears to be based on a misunderstanding of a paper my colleagues van Dam, Mosca and I wrote on “The power of adiabatic quantum computing”. That speed up unfortunately does not hold in the setting at hand, and therefore D-Wave’s “quantum computer” even if it turns out to be a true quantum computer, and even if it can be scaled to thousands of qubits, would likely not be more powerful than a cell phone.

Yours sincerely,
Umesh Vazirani
Roger A. Strauch Professor of Computer Science
Director, Berkeley Quantum Computing Center

(via Scott Aaronson)