A general framework for applying feedback control to quantum control system under continuous measurement by a probe is discussed. The analysis is the standard bilinear interacting hamiltonian control form. A continuous measurement model based on an interacting quantum probe is used to control via feedback. It is also shown that concepts from systems theory could be applied with non-trivial modifications to analyze such feedback control systems undergoing decoherence. We also report new progress to the ongoing work on applications of feedback to control decoherence in open quantum systems.
A general framework for applying feedback control to quantum control system under continuous measurement by a probe is discussed. The analysis is the standard bilinear interacting hamiltonian control form. A continuous measurement model based on an interacting quantum probe is used to control via feedback. It is also shown that concepts from systems theory could be applied with non-trivial modifications to analyze such feedback control systems undergoing decoherence. We also report new progress to the ongoing work on applications of feedback to control decoherence in open quantum systems.
In this work we propose a strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done. A construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with nontrivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and decoherence free subspaces. Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system must be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. In the subsequent section we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The analysis of continuous measurement on a decohering quantum system has not been extensively studied before. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free quantum computing. The results obtained are qualitatively different and superior to the ones obtained via master equations.
Abstract — Quantum feedback is assuming increasingly important role in quantum control and quantum information processing. In this work we analyze the application of such feedback techniques in eliminating decoherence in open quantum systems. In order to apply such system theoretic methods we first analyze the invariance properties of quadratic forms which corresponds to expected value of a measurement and present conditions for decouplability of measurement outputs of such time-varying open quantum systems from environmental effects. I.
Quantum feedback is assuming increasingly im- portant role in quantum control and quantum information processing. In this work we analyze the application of such feedback techniques in eliminating decoherence in open quan- tum systems. In order to apply such system theoretic methods we first analyze the invariance properties of quadratic forms which corresponds to expected value of a measurement and present conditions for decouplability of measurement outputs of such time-varying open quantum systems from environmental effects.
In this article we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The purpose of this information extraction is to determine the feedback in order to control decoherence based on an ``output equation", described by a bilinear form. An interacting bilinear form of control system is used instead of master equation to analyze the dynamic properties of the system. The analysis of continuous measurement on a decohering quantum system has not been extensively studied before.
This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of open quantum systems lead to the theory of continuous measurement and quantum trajectories, in which wave function collapse occurs over a finite time scale associated with an interaction. Within this formalism, it becomes possible to ask many new questions that would be trivial or even ill-defined in the context of the more basic measurement model. In this thesis, we investigate both theoretically and experimentally what fundamentally new capabilities arise when an experimental apparatus can resolve the continuous dynamics of a measurement. Theoretically, we show that when one can perform feedback operations on the timescale of the measurement process, the resulting tools provide significantly more control over entanglement generation, and in some settings can generate it optimally. We derive these results using a novel formalism which encompasses most known quantum feedback protocols. Experimentally, we show that continuous measurement allows one to observe the dynamics of a system undergoing simultaneous non-commuting measurements, which provides a reinterpretation of the Heisenberg uncertainty principle. Finally, we combine the theoretical focus on quantum feedback with the experimental capabilities of superconducting circuits to implement a feedback controlled quantum amplifier. The resulting system is capable of adaptive measurement, which we use to perform the first canonical phase measurement.