
FrAR 
Sala
degli Affreschi 
Quantum Control 
Invited Session 
Organizer: Sarlette, Alain 
Ghent Univ. 
Organizer: Ticozzi, Francesco 
Univ. di Padova 

10:3010:50, Paper FrAR.1 

Robust OpenLoop Stabilization of Fock States by TimeVarying Quantum Interactions (I) 
Sarlette, Alain 
Ghent Univ. 
Rouchon, Pierre 
MinesParisTech 
Keywords: Quantum control, Nonlinear control
Abstract: A quantum harmonic oscillator (spring subsystem) is stabilized towards a target Fock state by reservoir engineering. This passive and openloop stabilization works by consecutive and identical Hamiltonian interactions with auxiliary systems, here threelevel atoms (the auxiliary ladder subsystem), followed by a partial trace over these auxiliary atoms. A scalar control input governs the interaction, defining which atomic transition in the ladder subsystem is in resonance with the spring subsystem. We use it to build a timevarying interaction with individual atoms, that combines three noncommuting steps. We show that the resulting reservoir robustly stabilizes any initial spring state distributed between 0 and 4n+3 quanta of vibrations towards a pure target Fock state of vibration number n. The convergence proof relies on the construction of a strict Lyapunov function for the Kraus map induced by this reservoir setting on the spring subsystem. Simulations withÂ realistic parameters corresponding to the quantum electrodynamics setup at Ecole Normale Superieure further illustrate the robustness of the method.


10:5011:10, Paper FrAR.2 

On the Stability of Pointer States Using Lyapunov Theory (I) 
Somaraju, Ram Abhinav 
Vrije Univ. Brussel 
Petersen, Ian R 
Univ. of New South
Wales at the Australian Defence Force Academy 
Thienpont, Hugo 
Vrije Univ. Brussel 
Keywords: Quantum control, Hamiltonian dynamics, Conservation laws
Abstract: Pointer states are states of an open quantum system that are able to survive the constant monitoring of the system by an environment. It has been shown that open systems that are prepared in superpositions of such pointer states quickly decohere and evolve into classical statistical mixtures of (pure) pointer states. In this paper we demonstrate, using appropriate modeling assumptions for the system environment interaction, the following result: An individual trajectory of the system state involves towards a specific pointer state (and not just a statistical mixture of the same) if one monitors the environment state by measuring environmental observables even if only a fraction of these measurement outcomes are known to the observer. The central tool used to demonstrate this is the identification of conserved quantities that correspond to the eigenprojections of the systemenvironment Hamiltonian. We construct Lyapunov functions using this Hamiltonian to demonstrate the stability of the pointer states.


11:1011:30, Paper FrAR.3 

On the Role of Hamiltonians for Dissipative Entanglement Engineering (I) 
Ticozzi, Francesco 
Univ. di Padova 
Viola,Â Lorenza 
Dartmouth Coll. 
Keywords: Quantum control
Abstract: Determining whether an entangled state of interest can be asymptotically prepared by realistic opensystem dynamics has important applications across quantum engineering. This problem has been recently solved for purely dissipative quasilocal dynamics described by a continuoustime Markovian semigroup. Here, we extend our previous analysis by addressing the role of internal Hamiltonian dynamics as well as of Hamiltonian control resources for achieving the same task. We show how Hamiltonians that are not frustrationfree can genuinely extend the class of stabilizable states. In particular, we present stabilizing Hamiltonians, along with necessary and sufficient conditions for their existence, for maximally entangled GHZstates and translationally invariant Wstates, none of which are generally stabilizable by
dissipation alone.

11:3011:50, Paper
FrAR.4 

Which Notion of Energy for Bilinear Quantum Systems? (I) 
Boussa\EFd, Nabile 
Lab. de Math\E9matiques, Univ. de FrancheComt\E9 
Caponigro, Marco 
INRIA Nancy – Grand Est 
Chambrion, Thomas 
Univ. de Lorraine 
Keywords: Quantum control, Distributed parameter systems, Optimal control
Abstract: In this note we investigate what is the best L^pnorm in order to describe the relation between the evolution of the state of a bilinear quantum system with the L^pnorm of the external field. Although L^2 has a structure more easy to handle, the L^1 norm is more suitable for this purpose. Indeed for every p>1 it is possible to steer, with arbitrary precision, a generic bilinear quantum system from any eigenstate of the free Hamiltonian to any other with a control of arbitrary small L^p norm. Explicit optimal costs for the L^1 norm are computed on an example.


11:5012:10, Paper FrAR.5 

Exploring the Cooling Limit of Quantum Mechanical Oscillators Via Optimization (I) 
Wang, Xiaoting 
Univ. of Massachusetts Boston 
Vinjanampathy, Sai 
Univ. of Massachusetts Boston 
Strauch, Frederick 
Williams Coll. 
Jacobs, Kurt 
Univ. of Massachusetts Boston 
Keywords: Optimal control
Abstract: In this work, we have studied the optimal cooling limit when cooling a quantum mechanical oscillator by coupling it to an auxiliary. Since this limit is necessarily confined by the energy transfer rate of the control, i.e., the magnitude of the spectrum of the control Hamiltonian, we search for the optimal control Hamiltonian that can achieve the maximal cooling fidelity, given a bounded energy transfer rate. First we analyze and present a class of Hamiltonian which generates the perfect cooling result in the absence of decoherence. Then with perturbation analysis, we further show that such Hamiltonian is also optimal at least to the first order of the dynamical dissipative terms. With the help of numerical optimization, we have studied cases with different damping rates of the system and the auxiliary, and derived the plot of the optimal cooling fidelity curve versus time as well as the optimal time point to achieve the maximal fidelity.


12:1012:30, Paper FrAR.6 

Geometric Optimal Control of the Contrast Problem in Magnetic Resonance Imaging 
Sugny, Dominique 
Univ. of Bourgogne 
Lapert, Marc 
Univ. of Bourgogne 
Glaser, Steffen J. 
Tech. Univ. Muenchen (TUM) 
Keywords: Quantum control, Optimal control, Hamiltonian dynamics
Abstract: The control of the dynamics of spin systems by magnetic fields has opened intriguing possibilities in quantum computing and in Nuclear Magnetic Resonance spectroscopy. In this framework, optimal control theory has been used to design control fields able to realize a given task while minimizing a prescribed cost such as the energy of the field or the duration of the process. However, some of the powerful tools of optimal control had not been used yet for NMR applications in medical imagery. Here, we show that the geometric control theory approach can be advantageously combined with NMR methods to crucially optimize the imaging contrast. This approach is applied to a benchmark problem but it gives a strong evidence for the possibility of using optimal control theory for enhancing the contrast and the resolution of medical images.
