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Feedback control of spin systems Claudio Altafini

Summary: Feedback control of spin systems
Claudio Altafini
International School for Advanced Studies
via Beirut 2­4, 34014 Trieste, Italy
June 9, 2006
The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a
control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary
and deterministic closed loop. The Lyapunov­based feedback design presented does not require spins
that are selectively addressable. With this method, it is possible to obtain control inputs also for di#cult
tasks, like suppressing undesired couplings in identical spin systems.
1 Introduction
NMR spectroscopy deals with the manipulation of nuclear spins of quantum ensembles, see [2, 12]. These
systems exhibit most of the essential features of quantum mechanical systems, like the state space of tensorial
type (providing exponential growth of the degrees of freedom available) and natural coupling mechanisms
between spins, which guarantee the nonclassical nonlocality characteristic of quantum evolutions. For the
purposes of state manipulation, over the last 40 years the field of NMR has developed an extremely versatile
and universally accepted set of tools, in the form of sequences of electromagnetic pulses [12, 9, 16]. In terms


Source: Altafini, Claudio - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)


Collections: Engineering; Mathematics