In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem time optimal control unitary propagator. Radio frequency pulses are used in coherent to implement transfer state. Pulse that accomplish desired should be short possible order minimize effects relaxation and optimize sensitivity experiments. Here, give an analytical characterization such applicable coherence experiments multiple-spin systems. We have adopted general mathematical formulation, present many...

A parameterization of the density operator, a coherence vector representation, which uses basis orthogonal, traceless, Hermitian matrices is discussed. Using this we find region permissible vectors represent operator. The inequalities specify are shown to involve Casimir invariants group. In particular cases, allows determination degeneracies in spectrum identification also provides method constructing quantities invariant under {\it local} unitary operations. Several examples given...

In this article, we study a class of control problems which involves controlling continuum dynamical systems with different values parameters characterizing the system dynamics by using same signal. We call such <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">control</i> xmlns:xlink="http://www.w3.org/1999/xlink">of</i> xmlns:xlink="http://www.w3.org/1999/xlink">ensembles</i> . The motivation for looking into these comes from manipulation an...

Radio-frequency pulses are used in nuclear-magnetic-resonance spectroscopy to produce unitary transfer of states. Pulse sequences that accomplish a desired should be as short possible order minimize the effects relaxation, and optimize sensitivity experiments. Many coherence-transfer experiments NMR, involving network coupled spins, use temporary spin decoupling effective Hamiltonians. In this paper, we demonstrate significant time can saved producing an Hamiltonian if is avoided. We provide...

Finding control fields (pulse sequences) that can compensate for the dispersion in parameters governing evolution of a quantum system is an important problem coherent spectroscopy and information processing. The use composite pulses compensating dynamics widely known applied. In this paper, we make explicit key aspects makes such compensation possible. We highlight role Lie algebras noncommutativity design pulse sequence. Finally, investigate three common dispersions NMR spectroscopy, namely...

Abstract We describe in this article some key themes that emerged during a Caltech/AFOSR Workshop on ‘Principles and Applications of Control Quantum Systems’ (PRACQSYS), held 21–24 August 2004 at the California Institute Technology. This workshop brought together engineers, physicists applied mathematicians to construct an overview new challenges arise when applying constitutive methods control theory nanoscale systems whose behaviour is manifestly quantum. Its primary conclusions were...

In this paper, we demonstrate how optimal control methods can be used to speed up the implementation of modules quantum algorithms or simulations in networks coupled qubits. The gain is most prominent realistic cases, where qubits are not all mutually coupled. Thus shortest times obtained depend on coupling topology as well characteristic ratio time scales for local controls vs nonlocal (i.e., coupling) evolutions specific experimental setting. Relating these minimal number gives tightest...

Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations unitary gates under relaxation. The potential gain by optimal using relaxation parameters against time-optimal is explored and exemplified in numerical algebraic terms: it the method choice govern systems within subspaces weak whenever drift Hamiltonian would otherwise drive system through fast decaying modes. In a standard model generalising decoherence-free...

Dynamic programming algorithms are presented for automated generation of length minimizing geodesics and curves extremal curvature on the neocortex macaque visible human. Probabilistic models curve variation constructed in terms variability speed, curvature, torsion Frenet representation.

Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this article, we use principles of optimal theory establish physical limits how closely a system can be steered desired target state in the presence relaxation. particular, explicitly compute maximum amplitude coherence or polarization that transferred between coupled heteronuclear spins large molecules at high magnetic fields Very general decoherence mechanisms include...

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning as an example, it proves possible to significantly improve efficiency of while introducing robustness toward instrumental imperfections such radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations well practical on a 13Cα,15N-labeled powder glycine. demonstrate gain 53% for 15N 13Cα coherence transfer...