When I started writing children’s books, they were for my own children. Since I never stop singing the praises of science, I wasn’t much concerned about how scientifically literate they would be. But how am I doing outside my own family? I don’t know! That’s where you come it 😁
Something I lost sight of for a long time is the reason I study physics, or the reason I started studying it anyway. I got into it for no reason other than it was an exciting application of mathematics. I was in awe, not of science, but of the power of mathematics.
Now there are competing pressures. Sometimes I find myself “doing physics” for reasons that can only best be seen as practical. Fine—I’m a pragmatic person after all. But practicality here is often relative to a set of arbitrarily imposed constraints, such as requiring a CV full of publications in journals with the highest rank in order to be a good academic boi.
You may say that’s life. We all start with naive enthusiasm and end up doing monotonous things we don’t enjoy. But then we tell ourselves, and each other, lies about it being in service of some higher purpose. Scientists see it stated so often that they start to repeat it, and even start to believe it. I know I’ve written and repeated thoughtless platitudes about science many times. It’s almost necessary to convince yourself of these myths as you struggle through your school or your job. Why am I doing this, you wonder, because it certainly doesn’t feel rewarding in those moments.
On the other hand, many people are comfortable decoupling their passion from their job. Do the job to earn money which funds your true passions. Not all passions provide the immediate monetary returns one needs to live a comfortable life after all. So you can study science to learn the skills that someone will pay you to employ. There are many purely practical reasons to study physics, for example, which have nothing to do with answering to some higher calling. This certainly seems more honest than having to lie to yourself when expectations fail.
(I should point out that if you are one of those people currently struggling through graduate school, academia is not the only way—maybe not even the best way—to sate your hunger for knowledge, or just solve cool maths problems.)
A lot of scientists, teachers, and university recruiters get this wrong. There is a huge difference between being curious about nature and reality and suggesting it is morally good to devote one’s life to playing a small part in answering specific questions about such.
Einstein did not develop general relativity to usher in a new era of gravitational wave astronomy, as cool as that is. He did it because he was obsessed with answering his own questions driven by his insatiable imagination. Even the roots of the now enormous collaboration of scientists which detected gravitational waves started in a water cooler conversation among a few physicists, which is best summarized by this tweet:
In other words, we don’t actually do things through a consensual agreement about its potential value to a higher power called science. We think about doing certain things because we are curious, because we want to see what will happen, or because we can.
Like all other myths scientists and their adoring followers like to deride, science as a moral imperative is just that—a myth. Might we not get further with honesty, by telling ourselves and others that we are just people—people trying to do cool shit. The great things will come as they always have, emerging from complex interactions—not by everyone collectively following a blinding light at the end of tunnel, but by lighting the tunnel itself with millions of unique candles.
Two new papers were recently posted on the arXiv with my first two official PhD students since becoming a faculty member! The earlier paper is titled Efficient online quantum state estimation using a matrix-exponentiated gradient method by Akram Youssry and the more recent paper is Minimax quantum state estimation under Bregman divergence by Maria Quadeer. Both papers are co-authored by Marco Tomamichel and are on the topic of quantum tomography. If you want an expert’s summary of each, look no further than the abstracts. Here, I want to give a slightly more popular summary of the work.
This work is about a practical algorithm for online quantum tomography. Let’s unpack that. First, the term work. Akram did most of that. Algorithm can be understood to be synonymous with method or approach. It’s just a way, among many possibilities, to do a thing. The thing is called quantum tomography. It’s online because it works on-the-fly as opposed to after-the-fact.
Quantum tomography refers to the problem of assigning a description to physical system that is consistent with the laws of quantum physics. The context of the problem is one of data analysis. It is assumed that experiments on this to-be-determine physical system will be made and the results of measurements are all that will be available. From those measurement results, one needs to assign a mathematical object to the physical system, called the quantum state. So, another phrase for quantum tomography is quantum state estimation.
The laws of quantum physics are painfully abstract and tricky to deal with. Usually, then, quantum state estimation proceeds in two steps: first, get a crude idea of what’s going on, and then find something nearby which satisfies the quantum constraints. The new method we propose automatically satisfies the quantum constraints and is thus more efficient. Akram proved this and performed many simulations of the algorithm doing its thing.
This work is more theoretical. You might call it mathematical quantum statistics… quantum mathematical statistics? It doesn’t yet have a name. Anyway, it definitely has those three things in it. The topic is quantum tomography again, but the focus is different. Whereas for the above paper the problem was to devise an algorithm that works fast, the goal here was to understand what the best algorithm can achieve (independent of how fast it might be).
Work along these lines in the past considered a single figure of merit, the thing the defines what “best” means. In this work Maria looked at general figures of merit called Bregman divergences. She proved several theorems about the optimal algorithm and the optimal measurement strategy. For the smallest quantum system, a qubit, a complete answer was worked out in concrete detail.
Both Maria and Akram are presenting their work next week at AQIS 2018 in Nagoya, Japan.