6-th Volterra-CIRM International School
Quantum information: filtering and control
Centro V. Volterra Roma, Università di Roma Tor Vergata
Centro Internazionale per la Ricerca Matematica, Istituto Trentino di Cultura
with the sponsorship of
the International Association for Quantum Probability and Infinite dimensional Analysis
will deal with the three main aspects of quantum control:
I) Mathematical aspects: Introduction to classical and quantum control theory, quantum dynamical programming, measurement, filtering and feedback control.
II) Physical aspects: How to use the fundamental laws of nature to achieve optimal control of quantum systems? What are the fundamental limitations of controllability and observability in quantum world?
III) Experimental aspects: Engineering of experimental quantum devices to achieve pre-determined goals such as quantum gates and quantum programs. Focus here will be on specific case studies in the effort to make a bridge between theoretical results and concrete implementation.
In all lectures emphasis will be on concrete problems of quantum physics, technology and quantum information.
Abstract mathematical methods will be always illustrated with concrete and relevant problems and examples.
The level of the lectures will be suitable for graduate or postgraduate students in physics, mathematics, engineering, quantum information.
This is a preliminary programme: we are still waiting for a definitive answer from two additional main lecturers.
Viacheslav Belavkin, University of Nottingham
(I) Quantum Hamiltonian dynamics and programming control
Franco Fagnola, Università di Genova
Quantum Markov semigroups and control of the decoherence
Luigi Accardi, Università di Roma Torvergata
The stochastic limit of quantum theory for filtering and control
(I) The stochastic golden rule for dipole type Hamiltonians
(II) Stochastic limit approach to filtering
(III) The control through decoherence programme
(IV) Control through laser fields
(V) Coherent population trapping: entanglement and decoherence
control or filtering apparatus is based on the implicit or explicit exploitation
of some basic law of nature. By suitably acting on the environment, on
the boundary conditions,
on the choice of the materials and systems involved, ... the quantum engineer reduces these fundamental and universal interactions, to effective interactions which are very specific to the situation considered. The path leading from the fundamental laws to these effective interactions (phenomenological models) is often intricate and difficult to make esplicit. Some of the greatest triumphs of theoretical physics have gone precisely in this direction.
Recently the stochastic limit technique has been developed in order to automatize this deduction of effective models and has proven to have a wide range of applicability. The main goals of these lectures are:
i) to present the stochastic limit as the natural input to the filtering and control problem:
if you start from real physical equations rather than from phenomenological ones, you
gain a microscopic interpretation of the parameters involved, which is essential
to give a concrete meaning to the procedures devised to filter and control these parameters.
ii) to present the method of control by decoherence, which is implicit in most of the papers
of control of master equations, and to illustrate it with some basic examples taken
from quantum optics or solid state physics.
Mauro D'Ariano, Massimiliano Sacchi, Università di Pavia
Optimization in the design of quantum experiments
Andreas Boukas, American College of Greece
(a) Quantum stochastic control and associated stochastic Riccati equations
(b) Control of quantum Langevin equations
Calarco, University of Innsbruck
Coauthors: U. Dorner, P. Julienne, C. Williams, and P. Zoller
Exploiting quantum control for quantum computation in optical lattices:
marker atoms and molecular interactions
We develop a scheme for quantum computation with neutral atoms, based on the concept of "marker" atoms, i.e., auxiliary atoms that can be efficiently transported in state-independent periodic external traps to operate quantum gates between physically distant qubits. Quantum control theory (Krotov's method) is used to optimize the fidelity of both atom transport and quantum gate operations. This allows for relaxing a number of experimental constraints for quantum computation with neutral atoms in microscopic potential, including single-atom laser addressability. We discuss the advantages of this approach in a concrete physical scenario involving molecular interactions.
Pechen, Steklov Mathematical Institute Moscow
Control of atomic quantum states by lasers in the stochastic limit
limit method was developed by Accardi, Lu and Volovich for the investigation
of the dynamics of quantum systems interacting with environment. This method
allows to deduce in a simple way quantum white noise equations and quantum
stochastic differential equations for the dynamics of the total system
in the weak coupling and low density regimes. Taking partial expectation
of these equations one gets master equation for the reduced dynamics.
If the reservoir is in an equilibrium then the master equation under very general conditions describes decoherence, i.e., relaxation of the reduced density matrix to a diagonal in the basis of the free system Hamiltonian state, which usually is the equilibrium state with the same temperature as the reservoir.
The purpose of the talk is to consider instead of an equilibrium reservoir a coherent one. In physics it corresponds to lasers. We will apply the stochastic limit method to the investigation of an atom interacting with lasers, deduce the corresponding master equations and investigate in details coherent quantum control for the case of a three-level $\Lambda$-atom (with forbidden transition between the two lowest energy levels).
Hersch Rabitz, Princeton University
Problems of control in quantum physics and chemistry
Optimal control theory and the numerical issues involved, closed loop adaptive feedback concepts,
a summary of some of the current experiments going on, concepts for getting at the mechanisms of control, and concepts for Hamiltonian identification.
Sergienko, Boston University
Engineered entanglement: from quantum communication to quantum bio-physics
Quantum control and filtering: Experimental implementation
Four photon states engineering
The technique of producing four-photon entangled states in quantum optics using effect of spontaneous parametric down conversion (SPDC) in a sequence of two nonlinear crystals has been used extensively over the last ten years for demonstrating such intriguing no classical effects as quantum teleportation, entanglement swapping, entanglement purification.
Inside the nonlinear material the photon of laser radiation can disintegrate with some probability into pairs of orthogonally polarized photons propagating in two different directions.
When the very short femtosecond laser pulse passes through two nonlinear crystals, then pairs of photons emitted from such usually independent sources of spontaneous decay can demonstrate existence of stable phase relationship between all probability amplitudes and can be used for constructing and Engineering genuine four-photon entangled states.
The school will be held at Grand Hotel Bellavista in Levico Terme, 20 km. far from Trento. In the heart of the great itineraries between Venice-Verona and Bolzano-Innsbruck, Trento is a Renaissance town in the Alps. Roman town and bridge between the Italian and European culture, Trento shows in its beautiful monuments (the Castle Buonconsiglio, the Duomo, the houses decorated by frescoes) the Renaissance influence, inherited by the Prince Bishops, who ruled the town for eight centuries and made of Trento the seat of the XIX Ecumenical Council during the 16th century.
The cost for the participation to the six days' meeting is:
- Full board in a double bedroom Euro 324,80 (US $ 387,71).
- Full board in a single bedroom Euro 402,80 (US $ 480,82).
Participants can take part in an excursion on Wednesday afternoon. The lecture notes of the main lecturers and of the seminars will be available during the school.
Bus transportation will be provided from Trento railway station to the conference site on Saturday, July 3, at 20:30, and back to Trento railway station on Friday, July 9.
The deadline for registration is: June 15, 2004.
A restricted number of grants for financial support of either living or (in truly exceptional cases) travel expenses are available. The assignment of these grants will be decided by June 20.
Those interested to apply for such a grant should send via e-mail the Application form to: