Controllability analysis of quantum systems immersed within an engineered environment

Abstract

Abstract. The problem of controllability of quantum systems interacting with an engineered environment, whose dynamics are described by a non-Markowian master equation is addressed. The manipulations of the dynamics is realized with both a laser field and a tailored non-equilibrium, and generally time-dependent, state of the surrounding environment. Lie algebra theory is used to characterize the structures of the reachable state sets and to prove controllability. The theoretical results are supported by examples.

Trajectory tracking for non-Markovian quantum systems

“…Also, the deocoherence channels used in the scheme must be restricted by the real-world setting. In other words, the open quantum systems must be dynamically controllable [23,24]. Therefore, the selection on control parameters in our scheme, two principles have to be stuck up: (i).…”

Open quantum systems integrable by partial commutativity

“…In this article, we shall consider the evolution generator L(t) of d−level quantum systems in the form [26,27]:…”

Control of Quantum Systems

“…The quantum system (1) is said to be pure state controllable if for every pair of initial and final states j 0 i and j f i, there exist control functions fu k .t /g and a time T > 0 such that the corresponding solution of (1) with initial condition j 0 i satisfies j .T /i D j f i. 2014 Alternative definitions have also been considered for the controllability of the quantum system (1); e.g., see Albertini and D'Alessandro (2003) and Grigoriu et al (2013) in the case of open quantum systems. The following theorem provides a necessary and sufficient condition for pure state controllability in terms of the Lie algebra L 0 generated by the matrices f iH 0 ; iH 1 ; : : : ; iH m g, u.N / the Lie algebra corresponding to the unitary group of dimension N , su.N / the Lie algebra corresponding to the special unitary group of dimension N , sp.…”