Pole placement approach to coherent passive reservoir engineering for storing quantum information

Abstract

Reservoir engineering is the term used in quantum control and information technologies to describe manipulating the environment within which an open quantum system operates. Reservoir engineering is essential in applications where storing quantum information is required. From the control theory perspective, a quantum system is capable of storing quantum information if it possesses a so-called decoherence free subsystem (DFS). This paper explores pole placement techniques to facilitate synthesis of decoherence free subsystems via coherent quantum feedback control. We discuss limitations of the conventional 'open loop' approach and propose a constructive feedback design methodology for decoherence free subsystem engineering. It captures a quite general dynamic coherent feedback structure which allows systems with decoherence free modes to be synthesized from components which do not have such modes.

Synthesis of robust memory modes for linear quantum systems with unknown inputs

“…Inspired by the work [21,30,31], in this section, we will introduce the technique dealing with coherent robust pole placement including unknown input signals. Consider a linear quantum passive system as the plant whose dynamics are governed by the following…”

“…In the rest of this paper, we assume that the pair (A p , C † f ) is controllable and the pair (A p , C p ) is observable. According to the separation principle as discussed in [30], the eigenvalues of A p -C † f K and A p -LC p can be designed independently of each other given that…”

“…Pole placement within the scope of coherent feedback as depicted in Fig. 1 has been studied in our previous work, under a coherent observer-based framework [30,31]. Although the pole placement problem has been tackled in [30] by solving an algebraic equation, robust pole placement applied to the synthesis of memory modes in the presence of unknown inputs is not yet considered [21].…”

“…1 has been studied in our previous work, under a coherent observer-based framework [30,31]. Although the pole placement problem has been tackled in [30] by solving an algebraic equation, robust pole placement applied to the synthesis of memory modes in the presence of unknown inputs is not yet considered [21]. For practical quantum control systems, it is critical to attain robustness due to prevalent uncertainties in open quantum systems [32][33][34].…”

Fixed time steps discrete-time sliding mode consensus protocols for two degree of freedom helicopter systems

“…where s T si is the sliding mode gains for i th agent to be obtain using pole-placement approach (Nguyen et al, 2017), t is the sampling period of discrete-time system. From (12), the global sliding surface can be defined as…”