Over 6 months later

So it’s been over six months since I started this blog and I thought that this might be an appropriate moment to pause and reflect. During this time I’ve experienced several major changes culminating in a move to my new institution, the Wissenschaftskolleg zu Berlin where I’ll be a fellow for 2009/2010. These changes have been reflected in a serious lack of productivity for the past couple of months. Now that I’ve moved to Berlin and my fellowship is starting I’m hoping to reassess my involvement in open science via this blog. (And to try and restart my scientific contributions here.)

I originally started this blog for a variety of reasons, some noble, and some not so noble , including,

1. I wanted to experiment with this whole science 2.0 thing in the context of a theoretical science.
2. I wanted to silence the critics of open science (eg., by showing openness is no bad thing).
3. I wanted to create a new venue to disseminate my research agenda.
4. I wanted to find new collaborators and outsource (crowdsource?) expertise to solve my problems.

After 6 months or so on I feel that I am in a good position to assess how things have gone. So here goes.

1. Is there anything to this science 2.0 thing?

Yes and no: I’ve discovered some very interesting web tools to do all sorts of things which can help me to organise my scientific workflow. I really like bookmarking tools like del.icio.us. I also absolutely love tiddlywiki (although mine is sadly neglected of late); the nonlinear note-taking of tiddlywiki perfectly matches my approach to research. (I’m extremely curious to see if google wave will provide a more natural science 2.0 tool. I look forward to being able to participate when enough invites become available.)

However, I’ve discovered that other webtools (namely Twitter!!) insidiously (and seriously) fragment my concentration and free time.

(Now that I’m beginning my fellowship at the Wissenschaftskolleg I’m going to turn over a new leaf and completely shutoff internet access for several hours every day… I figure this might help me focus better.)

I’m less clear on blogging as a means of scientific outreach: I haven’t tried to seriously do this yet, but it occurs to me that this is an ideal medium.

2. On the criticisms of open science

There is one criticism of open science that I think, from my personal experience, is totally unfounded: that is the worry that people will “steal” your ideas. This certainly never happened to me over the past 6 months. I know this is a stupid argument, as I probably had nothing worth stealing etc. etc. But I also think, for other reasons, that it is an unfounded concern. Firstly, the blog posts are time stamped. Secondly, to actually steal an idea/result someone would probably have to write everything up carefully etc., and that, in itself, is hard work, which is rather unattractive. But this is all obvious.

However, this isn’t really the actual concern that critics have: the main worry that many of my colleagues express is not that someone will come and copy a solved problem from a post and make a paper, but rather that, if one was to post their favourite open problems openly, then someone else will solve them faster! Many people have expressed this concern to me.

Evidently, the currency of theoretical physics is not solved problems, but rather “solvable problems” coupled with a good intuition for how to solve them: I know lots (most?) of people who hoard interesting conjectures which are on the edge of solvability. These are the primary treasures of theoretical physics.

Open science asks you to reveal these treasures and, in the process, give up the intellectual credit for their solution; if someone quickly goes and solves the problem using your own suggested method and writes it up then all you’re likely to get in return is a citation for suggesting the problem and the argument. I have certainly experienced the frustration of posing a solvable problem and suggesting an appropriate method of solution only to find that someone else had gone and solved it using my suggested method, wrote it up, and didn’t even acknowledge our conversation.

There’s not much I can say here: I do believe this concern *is* justified. And since these treasured problems are potential papers, every time someone shares a solvable problem (+appropriate intuition for a solution) then one exposes oneself to a considerable risk of losing all credit for the potential paper.

In my experience, to first order , noone actually reads the scientific content on a blog. (This is pretty easily detected by looking at the blog stats, the “soft” posts always attract an order of magnitude more views.) This is natural: there are simply not many people who work in areas related to my work, and it would be presumptious to expect that everyone should read the technical posts. So the only rejoinder I can make to the criticism that sharing solvable problems is bad is that noone will read them.

3. The blog as a venue for a research agenda

Maybe. It certainly helps me: at conferences people now often know exactly what I’m thinking about and this helps conversations to start.

4. The blog as a means to find new collaborators?

No. This hasn’t helped me at all so far; I haven’t found a single new collaborator this way. Worse, most potential collaborators are quite hesitant at the prospect of having research posted online before it is complete.

Is this blog really open science?

No. I’ve had to withhold several research results from this blog. This is because of many reasons (eg. the project predated the start of the blog, my collaborators were unwilling, or I didn’t have enough time to type stuff up). So, sadly, I must confess that I’ve failed the purity test of open science…

Will truly open theoretical science ever eventuate?

My quick answer: no. Here’s why: I think we’re in a local optima which would require most scientists to simultaneously and completely change their behaviour in order to shift away from. What do I mean? As I discussed above: the currency of theoretical physics (at least) are “solvable problems+solution intuition”. If *everyone* shared there little stash of this treasures then I agree we’d live in utopian world where science would be advanced as quick as possible. Except, this global optima is unstable: all it takes is for a couple of scientists to “cheat” and hoard their solvable problems to get an edge on their colleagues and thus kick us away from this global optimum. (This is all preconditioned on papers being a metric for success in the scientific community. Yeah, I know that’s not correct but, hey, if you’ve ever sat on a hiring committee you’ll know it isn’t too far wrong.)

This is my simple intuition for why things will always stay the same. I know it’s pessimistic; but I can’t think of how to realistically create the conditions so that the global scientific optimum becomes stable. (Give increased credit to problem ideas? How?)

Where now?

I don’t know. I’ll probably go quiet again for a couple of weeks while I adjust to life here in Berlin. After that I hope to restart my research. However, I’m hoping to spend several months learning new stuff outside my area of expertise. This probably won’t produce many new results, hence, not many posts. But I’ll try and summarise my efforts here, if it fits naturally into my workflow…

Many thanks for your attention and your comments!

Dynamics of the Anderson model I

In this post I’d like to continue looking at the dynamics of disordered systems. In particular I want to discuss the dynamics of the basic discrete 1D Anderson within the approximation developed in the previous post. As we’ll see, this can be reduced to the solution of a partial integro-differential equation.

Information propagation through disordered quantum systems

In this post, which highlights work with Christian Burrell and Jens Eisert, I’d like to talk about disordered quantum systems again. In particular, I’d like to discuss the problem of what is meant by “localisation” for a strongly interacting quantum system. I’d also like to investigate the role of disorder in how information propagates through interacting quantum systems.

The purpose of this post is to introduce (or, rather, to emphasise) a way to quantitatively discuss the phenomena of localisation in strongly interacting quantum systems. The approach I’d like to propose here exploits ideas from the theory of quantum noise to approximate the dynamics of disordered quantum systems. To discuss this proposal I want to begin by reviewing the theory of information propagation through interacting quantum systems. Then I’ll show how ideas from the theory of quantum noise can be successfully exploited to calculate properties of the discrete Anderson model. I’ll then conclude by showing how this approach gives a definite prediction for what the dynamics of a disordered strongly interacting quantum system should look like. I have now spent a little time studying the literature on disordered systems and I haven’t been able to find anything that applies quantum noise techniques to disordered system in quite the way I describe here, but I may not have used the correct search phrases; any omission is therefore due to my ignorance. (I have found one article which appears to exploit related ideas, but this approach appears to throw out more terms than the one I describe here. Additionally, this approach seems to be difficult to generalise to strongly interacting lattice systems.)

Hiatus

We are entering the exam term here at Royal Holloway so I probably won’t have much time for any research or blogging over the next 4 weeks or so as I will be dealing with exam administration and marking exams…

Reading group: on the average number of real roots of a random algebraic equation, M. Kac

At the moment I am in between research projects: I am “working” on a bunch of old projects, some of which are many years old, but I haven’t had any new ideas for any of them in a long time and, hence, I haven’t made any progress whatsoever. At the same time I am thinking about beginning work on some new projects. Most notably, I want to spend some time understanding quantum systems with static and annealed disorder, and the connections between these systems and computational complexity. Unfortunately the literature on disordered quantum systems is vast, to say the least. Hence, I am putting off learning it. So now I am procrastinating by learning about a whole bunch of new ideas in the hope of learning something that will make the entry into the disordered systems literature a little smoother.

Basically I am now going to play out my learning curve through this blog.

The type of problems I eventually hope to study will be of the following form. Take some family of computational problems , and consider a random instance from this family. What is the running time, on average, of some quantum algorithm to solve the problem? At the same time I’d also like to consider families of quantum problems (eg. a family of quantum systems) and understand the running time, on average, of either classical or quantum algorithms to calculate approximations to, eg., expectation values of local observables, of a random instance. In both cases there is obviously some quantum system (i.e., the quantum computer in the first case, and the quantum system studied in the second case), and there is obviously some disorder present. The hope, broadly speaking, is to exploit the ubiquitous phenomenon of Anderson localisation to understand what happens in each case.

However, except in some very special cases, the problems I want to study don’t reduce in any obvious way to systems studied in the disordered quantum systems literature (at least, not so far as I can see). So I’m now casting around looking for interesting stuff which might have some relevance…

At the most abstract and high level all of the problems I want to eventually consider require that one understands the critical points of a random function (which is usually related to the running time). With a bit of luck one will be able write this expression as a polynomial. Hence it’d be nice to understand, say, the roots of random polynomials.

Hamiltonian complexity talk

On Tuesday I gave a talk at the IMA conference at the IMS. I’ve put the slides here (it is a huge file, alas, as I included lots of pictures…) 

In this talk I took the opportunity to popularise a problem that I hope will provide a fruitful avenue for future research in the emergent field of hamiltonian complexity.

Before I describe this problem, I’d like to say a couple of words about hamiltonian complexity itself: this field, which gained considerable momentum last year thanks to a couple of tightly focussed workshops at Leiden and Santa Fe, is (roughly speaking) aimed at exploring the interplay between theoretical physics and computational complexity theory. The central question of hamiltonian complexity, I would argue, is: “how hard is it to simulate a physical system?” To actually answer this question quantitatively requires that we be rather careful about what we mean by ”physical system”, “simulation”, and ”hardness”.

For “physical system” it has been convenient for quantum information theorists to focus on quantum spin systems (i.e., a set of quantum spins arrayed in a low-dimensional lattice). Thus we say the size of such a system is . (Note, however, that the dimension of the hilbert space of such a system scales at least as fast as .)  

For “simulation” we typically mean a classical computer carrying out some algorithm, although one could widen this definition. To count as a simulation the algorithm in question needs to be able to calculate a prediction for some physical observable.

For “hardness”, the field of computational complexity provides a now-standard framework to make this precise: one quantifies the temporal and spatial resources (measured in arithmetic operations and bits, respectively) required by a computation to carry out the desired task. 

With these ingredients in hand we can now state the main problem of hamiltonian complexity (well, of theoretical physics, really):

The simulation problem (equilibrium).

Input: A hamiltonian for a system of size ; an observable ; a tolerance ; a temperature .

Output: an approximation to the expectation value which satisfies .

The simulation problem, as stated, is simply the task of making a prediction for some observable. Hamiltonian complexity theory adds another dimension to the simulation problem by asking how hard it is to actually calculate such a prediction. This is clearly an important question: after all, suppose it took fundamental arithmetic operations to make a prediction for some experimentally accessible observable . This would be a disaster; even for 50 spins, one would need to perform operations, which is clearly unfeasible. So we’d have to give up on making any predictions whatsoever for such systems!

Obviously physicists are very good at making predictions, so this nightmare scenario never really occurs in practice. Hamiltonian complexity is thus aimed at explaining why this is the case. This is far from trivial because it is now relatively straightforward to write down 1D quantum spin systems whose equilibrium properties really do require something like arithmetic operations to approximate to within fairly reasonable tolerances! (We heard a lot about the state of the art of these results on Tuesday.)

Hamiltonian complexity is broken up into many sub-fields aimed at understanding variations on the theme of simulation and complexity. There are many subtle and profound techniques that have been developed to construct semi-realistic systems whose physical properties are hard to approximate. And there is yet another set of approaches aimed at actually simulating real (and imaginary) physical systems.

My talk was aimed at describing some situations where we actually can make predictions about quantum spin systems. I described two different situations where physical properties can be efficiently (on a classical computer) predicted. Typically — and the results I described are no exception — a proof that a physical property can be efficiently simulated actually provides a provably efficient algorithm to calculate the prediction. 

What I feel is the most interesting open question now is to understand better the interplay between the observables one wishes to simulate and the hamiltonian to be simulated. I think this adds a new layer of richness to the complexity-theoretic landscape for quantum spin systems: most work to date has focussed on the LOCAL HAMILTONIAN PROBLEM, which is a special case of the SIMULATION PROBLEM, above (by only demanding predictions for the observable itself). However, it is completely plausible that if you aren’t interested in the energy, but some other observable , the LOCAL HAMILTONIAN PROBLEM may become easier or harder!

TiddlyWiki

I’ve just started a TiddlyWiki hosted at tiddlyspot. I’ve also added a widget for the rss feed it generates to the sidebar. Content is light right now: I’ve only written a couple of tiddlers so far. This should increase in time.

I’ve done this for a couple of reasons. Firstly, the blog medium isn’t quite right for the style of research I now do: I no longer have the luxury to think in a linear fashion about one problem for an extended amount of time (I used to). I initially thought that the blog medium would allow me to recapture this style of working. Instead, more and more, I’m thinking nonlinearly about loads of little things in parallel. (This is probably really inefficient!) It is essentially impossible to write blog posts about these little things as, without extensive work, they lack any context. My hope is that the TiddlyWiki will provide a means organise and to allow open access to these contextless chunks of microcontent.

Secondly, I can use the TiddlyWiki to put all sorts of research-related stuff online which would simply be inappropriate in a blog post, eg., a definition I want to remember, a note on an improved proof of a result in a paper, notes on a talk, etc. None of these things would warrant a blog post, but all of them could be useful to someone, somewhere. I’m encouraged that Garrett Lisi has already mastered this approach.

Thirdly, I really like the way TiddlyWiki is so easy to edit, and how it provides such a convenient non-linear way of organising stuff. I only “got” tags a couple of months ago and now I think they are absolutely essential. 

I wonder where the future lies? At the moment all these web 2.0 tools aren’t quite right for the kind of theoretical open science that I’m doing: integration isn’t smooth between all the services (essentially, unevenly implemented widgets and rss are the only way these services can talk to each other). When I collect my thoughts a bit better I might write a bit more about content integration/synchronisation between web 2.0 services.

Buzzwords competition

So this post is part cynical, part hopeful dreaming.

Have you ever wondered if there was an algorithm for a successful paper? By “successful” I don’t necessarily mean profound, correct, or well-written. What I mean is that people talk about the paper, people cite it, and people get excited (either positively or negatively) about it.

Is this kind of success good for science? Maybe not. But I bet it is good for career development.

I’m sure that success as defined here isn’t really due to some algorithmic process (just as I’m sure there is no good algorithm to get a #1 song), but I am convinced that there are precise strategies to increase the probability that a paper (or, indeed, a song) is successful. In the context of scientific grants these strategies are collectively referred to as “grantsmanship”. Some people are just good at this: you know who they are, they publish dozens of PRLs per year and are regularly headlining important international conferences

What are these amazing strategies? Well, I really don’t know: I can see when someone is good at using these strategies, but I haven’t really been able to understand them…

However, there are one or two things that seem obvious: the ability to combine currently fashionable buzzwords in the title of the paper is a good one. Is this a good algorithm to get a successful paper? Surely not! Isn’t science about pure research, high morals, and a disinterested furthering of mankind’s collective knowledge?

Hmmm…

Perhaps we can test this hypothesis?

Translation-invariant quantum states

In making my research open I’ve continually encountered the difficulty of working out what to actually post. My typing speed doesn’t really match the speed at which I write down notes. In order to overcome this I’ve already censored most of the worst mistakes in my handwritten notes: i.e., I’ve spared you all of the crossed-out calculations where I made, eg., a minus-sign error and just written up the corrected notes. But apart from this you are pretty much getting what I’m thinking. There is an exception: I am involved in several projects where my co-authors have, for good reasons, requested I not post on them.

In writing my notes for a wider audience I also attempt to preface each post with some kind of general discussion. This seems to be a useful device, not unlike when using del.icio.us where you are forced to write a description. These little extra tasks seem like a useful mental filing device. Also, I think of the prefaces and tags etc. as a way to enthuse a wider audience to work on the problems I’m working on. (Not entirely clear if this is working yet…)

In this post I’d like to talk about a problem that I’m not really working on, but plan one day to work on if I have an idea. I guess most researchers have these kind of “to do” lists of problems waiting for time/inspiration. I find that these problems take up a lot of mental space (even when I’m not thinking about them directly: eg. “I must remember to think about problem X”) and I’d like to experiment by posting about one of them here in an attempt to clear out this to-do list, so to speak.

The problem/idea I’d like to talk about today is principally motivated by a single figure (Figure 1) in a paper of Cirac and Verstraete.

Solving symmetric disordered systems

In this post I want to describe a solution to a special class of symmetric disordered quantum systems. This solution is probably not new (it is pretty hard to come up with any solvable system which hasn’t been discovered before!) but I haven’t been able to find anything quite like it in a preliminary search of the literature. So I thought I’d write it up here; if anyone has seen something like this before then please let me know!

This research is intended to be part of a larger project focussed on the computational complexity of disordered quantum systems: I’m starting by collecting results on solvable models to subsequently utilise in the analysis of algorithms like the density matrix renormalisation group.