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We introduce a general framework, based on collision models and discrete CP-maps, to describe on an equal footing coherent and measurement-based feedback control of quantum mechanical systems. We apply our framework to prominent tasks in…
Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of Lindbald-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback…
The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering. In this paper we build on the ideas presented by…
A Markovian model for a quantum automata, i.e. an open quantum dynamical discrete-time system with input and output channels and a feedback, is described. A dynamical theory of quantum discrete-time adaptive measurements and multi-stage…
Measurement-based control, utilizing an active feedback loop, is a standard tool in technology. Feedback control is also emerging as a useful and fundamental tool in quantum technology and in related fundamental studies, where it can be…
We present a broad summary of research involving the application of quantum feedback control techniques to optical set-ups, from the early enhancement of optical amplitude squeezing to the recent stabilisation of photon number states in a…
We show that applying feedback and weak measurements to a quantum system induces phase transitions beyond the dissipative ones. Feedback enables controlling essentially quantum properties of the transition, i.e., its critical exponent, as…
While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, an intriguing situation in quantum systems, namely under continuous feedback, remains to be investigated. In this…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
We give an introduction to feedback control in quantum systems, as well as an overview of the variety of applications which have been explored to date. This introductory review is aimed primarily at control theorists unfamiliar with quantum…
Measurement feedback is a versatile and powerful tool, although its performance is limited by several practical imperfections resulting from classical components. This paper shows that, for some typical quantum feedback control problems for…
Feedback control of quantum systems via continuous measurement involves complex nonlinear dynamics. Except in very special cases, even for a single qubit optimal feedback protocols are unknown. Not even do intuitive candidates exist for…
Quantum transport is the study of the motion of electrons through nano-scale structures small enough that quantum effects are important. In this contribution I review recent theoretical proposals to use the techniques of quantum feedback…
Quantum feedback is a technique for measuring a qubit and applying appropriate feedback depending on the measurement results. Here, we propose a new on-chip quantum feedback method where the measurement-result information is not taken from…
Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum…
In this paper, we consider the feedback stabilization problem for N-level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools, we provide sufficient conditions on the…
Quantum measurement is essential to both the foundations and practical applications of quantum information science. Among many possible models of quantum measurement, feedback measurements that dynamically update their physical structure…
The limits of quantum feedback control have immediate consequences for quantum information science at large, yet remain largely unexplored. Here, we combine quantum filtering theory and moment-sum-of-squares techniques to construct a…
The effectiveness of measurement-based feedback control (MBFC) protocols is hampered by the presence of measurement noise, which affects the ability to accurately infer the underlying dynamics of a quantum system from noisy continuous…
Understanding and controlling engineered quantum systems is key to developing practical quantum technology. However, given the current technological limitations, such as fabrication imperfections and environmental noise, this is not always…