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Francesco Ticozzi

Publications and source records attributed to Francesco Ticozzi.

63 records · Page 4Linked to original sources
arXiv2009

On the convergence of an efficient algorithm for Kullback-Leibler approximation of spectral densities

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler pseudo-distance, which gives rise to a convex optimization problem. After developing the variational analysis, we discuss the properties of an efficient algorithm for the solution of the corresponding dual problem, based on the iteration of a nonlinear map in a bounded subset of the dual space. Our main result is the proof of local convergence of the latter, established as a consequence of the Central Manifold Theorem. Supported by numerical evidence, we conjecture that, in the mentioned bounded set, the convergence is actually global.

math.OC↗
arXiv2009

Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition

We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing the system in pure states or subspace codes. We provide a linear-algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace. We then construct a design algorithm for discrete-time feedback control that allows to stabilize a target subspace, proving that if the control problem is feasible, then the algorithm returns an effective control choice. In order to prove this result, a canonical QR matrix decomposition is derived, and also used to establish the control scheme potential for the simulation of open-system dynamics.

quant-ph↗
arXiv2009

Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space

The theory of Schroedinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path space maximum entropy problems is obtained from the a priori model in both cases via a suitable multiplicative functional transformation. In the quantum case, nonequilibrium time reversal of quantum channels is discussed and space-time harmonic processes are introduced.

math-ph↗
arXiv2008

Analysis and synthesis of attractive quantum Markovian dynamics

We propose a general framework for investigating a large class of stabilization problems in Markovian quantum systems. Building on the notions of invariant and attractive quantum subsystem, we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics. Our general analysis results are exploited to assess the ability of open-loop Hamiltonian and output-feedback control strategies to synthesize Markovian generators which stabilize a target subsystem, subspace, or pure-state. In particular, we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite-dimensional Markovian systems, that leads to a constructive strategy for designing the relevant controllers. Implications for stabilization of entangled pure states are addressed by example.

quant-ph↗
arXiv2008

Quantum Markovian Subsystems: Invariance, Attractivity, and Control

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.

quant-ph↗
arXiv2006

Single-bit Feedback and Quantum Dynamical Decoupling

Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or non-unitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dimensional target system, we show how by appropriately combining quantum feedback with dynamical decoupling methods, concatenated feedback-decoupling schemes may be built, which can operate under relaxed control assumptions and can outperform purely closed-loop and open-loop protocols.

quant-ph↗
arXiv2005

Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics

We propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.

quant-ph↗
arXiv2003

Robust Steering of n-level Quantum Systems

Robust open-loop steering of a finite-dimensional quantum system is a central problem in a growing number of applications of information engineering. In the present paper, we reformulate the problem in the classical control-theoretic setting, and provide a precise definition of {\em robustness} of the control strategy. We then discuss and compare some significant problems from NMR in the light of the given definition. We obtain quantitative results that are consistent with the qualitative ones available in the physics literature.

quant-ph↗