title: Toward Scalable Control of Open Quantum Systems
Creators: name: Chalermpusitarak, Teerawat
Publisher: name: Griffith University
Year: 2024
Subjects: subject: quantum control
subject: open quantum system
subject: quantum noise spectroscopy

description: An open quantum system is composed of a quantum system of interest that one can control and extract information, and its environment that is uncontrollable and directly inaccessible. The environment acts as a source of noise, which influences the dynamics of the system in an undesirable way. With the advanced development of quantum technologies, the need to precisely control the quantum system has become more dramatic. Dynamical error suppression techniques, such as dynamical decoupling and quantum optimal control techniques, have emerged as key tools to mitigate the effect of noise and improve the quality of control. Importantly, they rely on some degree of knowledge about the environment in order to succeed in suppressing the noise. Therefore, noise characterization is a crucial step before deploying any dynamical error suppression tools. It can be shown that the environment affects the dynamics of the system of interest via its noise correlation functions, or equivalently the polyspectra. Thus, these quantities are what can be learned from the system's dynamics in the presence of control. The protocols for characterizing the noise in this way fall under the umbrella of quantum noise spectroscopy. Historically, most of these protocols have been restricted to characterizing classical noise processes affecting the quantum system of interest, mostly due to the difficulty of moving beyond this limit. Ideally, however, one would like to have spectroscopy protocols capable of characterizing arbitrary noise, such as the one that may be present in a real quantum device. Thus, there is a need to generalize existing quantum noise spectroscopy protocols. Only in this way, the information they provide will be useful to predict and eventually control realistic noisy quantum systems. In the first part of this thesis, we study the implications of having a quantum environment interacting with a system. We find that the quantum environment can generate correlations with a rich structure that prevents the direct application of existing spectroscopy protocols for classical noises. Specifically, we show that the polyspectra of the quantum noise can be non-smooth functions with Dirac delta-like constraints originating from the multiple nontrivial ways in which the stationary constraint can be satisfied. Accounting for these issues, we modify the original quantum noise spectroscopy protocol to be able to characterize the polyspectra of quantum noise. We consider the bosonic environment as an example model but identify the presence of delta sub-constraints as a key obstacle in the characterization of arbitrary noise processes in the frequency domain. In the second part of this thesis, we realize that characterization for the sake of identifying the full representation of the system's dynamics is perhaps too ambitious and not necessary if the goal is to control the system. Indeed, the characterization task is much simpler when the objective is control. For most optimal control protocols, one has to specify one's control capabilities and find the optimal control based on such capabilities. In other words, the type of control that one can implement is limited. This limited control also means that only partial information about the environment is necessary given a fixed control capability. With this intuition, we develop a framework for characterizing only the relevant component of the noise relative to one's control capabilities and show that this information is necessary and sufficient for predicting and controlling the dynamics of a qubit under arbitrary noise. In the last part of this thesis, we aim to develop an approach to use the characterized noise correlation functions to predict the dynamics of the system. The primary advantage of our approach is that it avoids using knowledge of the Hamiltonian of the environment and the bath state, which are typically assumed but cannot be experimentally verified. In addition, our approach is based on propagating not only the system information but also the relevant information about the environment, i.e., noise correlation functions through time, and thus does not keep track of the bath state. We show that we can predict the behavior of the system for longer times, as compared to existing tools such as various types of master equations with the same initial information, i.e., with the same perturbative order.