General introduction to optimal control theory and how to control matter at the quantum level

David Tannor gave the Director’s Blackboard Talk at KITP today:

Quantum Control: From Chemistry to Cooling to Computing

Very nice talk, goes on a bit in the middle talking about the time dependent quantum mechanical picture vs use of phase control.

Very nice finish on mathematics of optimal control theory and the physical picture of how to use variational schemes to implement practical control.

Things I took away from this:

optimal control theory is underway but has a lot of open interesting questions;

there are theoretical techniques for implementing locally optimal control at the molecular level (and better, since similar technique permit high fidelity control of nuclear spins, individually and in ensemble);

the degree of controllability is quantifiable and may be complete for real systems;
(with the caveat that optimization has a divergent path which takes the system to infinite energy and imposing a penalty function my bias the search space)

there are clear technology paths for implementing real control over real systems;

this means phase control over molecular and atomic dynamics, including dissociation and association, at the individual atom and ensemble level, with high yield;

it may also be possible to control quantum coherence of mesoscopic pieces of material for interestingly long times;

it really all boils down to whether commutators of perturbed hamiltonians span the space of n*n hermitian matrices… or whether the Lie algebra is irreducable;

there are nice classical analogies on ergodicity, recurrence and disconnected compact phase spaces;

I would worry a bit about asymptotic states, non-local optimization, and whether additional perturbations of the hamiltonians can complete the system – ie if you have a system that is not completely controllable, can you impose a deliberate perturbation which changes it to a similar but completely controllable system;

long term goal – put some stuff into a cavity in a machine, tell the machine what you want the stuff to become, inject some energy in carefully sculpted and timed pulses, and with some reasonable efficiency get exactly what you want out, down to the atom or even the spin of the nucleus within the atom;

you can use this, in principle, eventually, to do cool stuff, like clean controlled chemistry, controlled coherence, and preparing qubits;

oh, and this is totally fucking awesome!


  1. #1 Brad
    May 4, 2009

    Quantum control theory!?!

    Yea, this could be amazing!

  2. #2 Robert P.
    May 9, 2009

    David Tannor is a sort of academic cousin of mine (his Ph.D. advisor was my postdoc advisor.) Remarkably creative, a real lateral thinker. And he’s got an Erdos number of 2.

  3. #3 Jonathan Vos Post
    May 9, 2009

    For the Erdos-challenged: Tannor, David J., coauthored a Math paper with Salamon, Peter, who in 1988 coauthored a Math paper with Paul Erdos.

  4. #4 Jonathan Vos Post
    May 9, 2009

    Sorry about those spurious hotlinks. We await a quantum computer to extend the following results. The collaboration graph C (constructed from about 1.9 million authored items in the Math Reviews database)has the roughly 401,000 authors as its vertices, with an edge between every pair of people who have a joint publication (with or without other coauthors — but see below for a discussion of “Erdös number of the second kind”, where we restrict links to just two-author papers). The entire graph has about 676,000 edges, so the average number of collaborators per person is 3.36. (If we were to view C as a multigraph, with one edge between two vertices for each paper in which they collaborated, then there would be about 1,300,000 edges, for an average of 6.55 collaborations per person.) In C there is one large component consisting of about 268,000 vertices. Of the remaining 133,000 authors, 84,000 of them have written no joint papers (these are isolated vertices in C). The average number of collaborators for people who have collaborated is 4.25; the average number of collaborators for people in the large component is 4.73; and the average number of collaborators for people who have collaborated but are not in the large component is 1.65.