Environment as a resource for controlling quantum systems

Quantum systems which are used for quantum technologies are typically open, i.e. interacting with their surrounding environment. While the environment is often considered as an obstacle for controlling such systems, in some cases it can be exploited as a useful resource. One approach was proposed in [1] and is known as incoherent control by the environment. In this talk, we discuss applications of coherent control by lasers and incoherent control by the environment to open quantum systems. First we discuss rigorous results on determination of the reachable states for a qubit interacting with the environment [2]. Then we outline recent rigorous results about use of the speed gradient gradient approach for coherent and incoherent control of quantum oscillator [3]. We also discuss recent results on gradient search of incoherent controls for various quantum systems (in preparation).
[1] A. Pechen, H. Rabitz, Teaching the environment to control quantum systems, Phys. Rev. A 73, 062102 (2006).
[2] L. Lokutsievskiy, A. Pechen, Reachable sets for two-level open quantum systems driven by coherent and incoherent controls, J. Phys. A 54, 395304 (2021).
[3] A. Pechen, S. Borisenok, A.L. Fradkov, Energy control in a quantum oscillator using coherent control and engineered environment, Chaos Solitons & Fractals 164, 112687 (2022).