A QIG seminar on “Approximating Polynomial Optimizations” by David Reeb

June 6, 2016

The quantum information group, Hannover, organises a regular group seminar where members have the opportunity to speak on a variety of themes from communicating early new results, to general interest topics such as reviews of interesting new papers.

In this post I’d like to highlght a video we’ve uploaded of a recent talk by David Reeb on “Approximating Polynomial Optimizations” via semidefinite programs:

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Advanced quantum theory

June 6, 2016

This summer semester (2016) I am giving a course on advanced quantum theory. This course is intended for theorists with familiarity with basic textbook single-particle quantum mechanics. The main objective is to understand how to study many interacting particles within QM. We will cover second quantisation, scattering theory, and some elementary relativistic quantum mechanics.

The course is now well under way and there are already several lectures available on youtube in the following playlist. I’ll be posting the rest there as the course develops.

 


The variational principle in quantum mechanics, lectures 9 and 10

June 23, 2011

In lecture 9 we continued reading the papers on matrix product states that we began in lectures 7 and 8.

1. Lecture 10: the time-dependent variational principle

In this lecture we will discuss the time-dependent variation principle (TDVP), which is a powerful method to simulate the nonequilibrium dynamics of a general quantum system while remaining within a given variational class. The TDVP is due, as far as I’m aware, to Dirac. Additionally, describing the TDVP isn’t especially difficult, so it is rather surprising that this elegant method it hasn’t made into standard textbooks. The general framework of the time-dependent variational principle can be found in [P. Kramer and M. Saraceno, Geometry of the Time-Dependent Variational Principle in Quantum Mechanics (Springer-Verlag, Berlin) (1981)].

These notes can be found in pdf format here.

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The variational principle in quantum mechanics, lecture 3

April 25, 2011

1. Lecture 3: The many body problem

In this lecture the many body problem is introduced in the context of first and second quantisation. The lecture notes can also be found here in pdf format.

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The variational principle in quantum mechanics, lecture 1

April 10, 2011

After another long hiatus I’ll be back to more regular blogging: I’m teaching a course entitled the variational principle in quantum mechanics for the summer semester here at the ITP Hannover, and I’ll be posting the notes. I hope to post other things along the way as there are many exciting developments I would like to mention…

Please feel free to comment or make suggestions on the lecture notes, I would sincerely appreciate your feedback! Read the rest of this entry »


QUEST special lecture 1

October 28, 2010

Yesterday I gave the first of three QUEST special lectures. You can find the slides here. Readers of this blog will be familiar with the content: I talked about the simulation problem and hamiltonian complexity and ended with the result that the dynamics of a 1D quantum spin system can be efficiently approximated (by a quantum cellular automaton) for |t| \sim \log(n).

In the next lecture I’ll show how to turn this result around and use quantum circuits to simulate the statics and dynamics of strongly interacting quantum systems via the variational principle.


The authorship contract

October 23, 2010

Put two physicists together and sooner or later the conversation will probably turn to complaining 😉 Most likely, the complaints will centre on journals or priority/authorship. I don’t know if mathematicians or biologists or other scientists complain like this, but I’ve sure been involved in plenty of conversations with physicists where we end up whining about author ordering and recognition for contributions to papers.

The story is somehow always the same: person X and person Y have a conversation. Person X tells person Y about some problem. Person Y gets enthused, asks lots of helpful questions, offers suggestions, and maybe works out a couple of small answers. Then X and Y go their separate ways and Y forgets the conversation. After 6 months of hard toil, person X realises that the problem was really a whole lot more subtle than X or Y originally though, but manages to solve the problem using a variety of clever new techniques and new ideas. The influence of the initial discussion is apparent, but much more had to be added to make it work. Person X then triumphantly writes a paper and sends it to Y for comments. But, uh oh! Person Y is extremely offended: Y is not an author! How dare X not offer Y authorship! In the ensuing unpleasantness X makes Y an author so as not to create enemies. The paper is submitted but X and Y do not feel entirely happy.

I have been X and I have been Y (and Z etc…) In the narrative I’ve given here Y clearly seems to be the baddie. But sometimes all the new ideas X came up with are, to Y, trivial. So who is the real baddie? Maybe X and Y are both wrong?

I actually see more than one problem here. Firstly, especially in physics, it is hard to weigh up a good idea vs. hard toil. Sometimes a really good idea, easily communicated during a dinner conversation, can lead to major new results to get a paper. But the hard toil is always an important component. How to weigh these two very different contributions? The second problem is that our recollections of conversations that have taken place can differ greatly: it is natural to see oneself as the major contributor in a conversation. But not everyone can be the a major contributor (i.e., we can’t all have had the crucial idea!) I’m reminded of the quote from the television series Yes Minister:

It is characteristic of all committee discussions and decisions that every member has a vivid recollection of them, and that every member’s recollection of them differs violently from every other member’s recollection; consequently we accept the convention that the official decisions are those and only those which have been officially recorded in the minutes by the officials; from which it emerges with elegant inevitability, that any decision which has been officially reached would have been officially recorded in the minutes by the officials, and any decisions which is not recorded in the minutes by the officials has not been officially reached, even if one or more members believe they can recollect it; so in this particular case, if the decision would have been officially reached, it would have been recorded in the minutes by the officials and it isn’t so it wasn’t.

Alas, it is not usual to take minutes of dinner-table conversations at physics conferences.

How to solve these problems? I don’t have any real ideas. But here’s a suggestion, inspired by something the mathematicians Hardy and Littlewood employed. Why not agree on a verbal contract at the end of any research discussion. I don’t mean anything too elaborate. I am simply proposing that, at the conclusion of their initial discussion, X and Y should have said something like:

“How about we agree that whatever happens from now on we will both be authors on whatever publications arise from this discussion. How about we proceed using Hardy-Littlewood rules?”

At least this way both X and Y know where they stand. If Y doesn’t pull his/her weight then, well, that’s another problem 😉

Perhaps this should be called the authorship pre-nup. What do you think?