The ability to optimally control quantum systems in the presence of environmentally-induced decoherence is important for many physical and chemical problems.We discuss both theoretical and experimental aspects of optimal control of open quantum systems. The theoretical analysis is based on fundamental concepts of open-system controllability and control landscapes. These theoretical advances lay the groundwork for practical applications, including numerical simulations and experimental implementations of adaptive feedback control. In particular, the adaptive approach was utilized to implement coherent control of decoherence, which uses coherent (unitary) preparation and manipulation of an open quantum system to significantly alter its incoherent (non-unitary) dynamics caused by coupling to an environment. We also discuss other applications, including optimal dynamic discrimination of similar quantum systems and optimal control of high-fidelity quantum gates in the presence of decoherence.
The ability to optimally control quantum systems in the presence of environmentally-induced decoherence is important for many physical and chemical problems.We discuss both theoretical and experimental aspects of optimal control of open quantum systems. The theoretical analysis is based on fundamental concepts of open-system controllability and control landscapes. These theoretical advances lay the groundwork for practical applications, including numerical simulations and experimental implementations of adaptive feedback control. In particular, the adaptive approach was utilized to implement coherent control of decoherence, which uses coherent (unitary) preparation and manipulation of an open quantum system to significantly alter its incoherent (non-unitary) dynamics caused by coupling to an environment. We also discuss other applications, including optimal dynamic discrimination of similar quantum systems and optimal control of high-fidelity quantum gates in the presence of decoherence.
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge of preserving relevant nonclassical features at the level of device operation. A major obstacle is decoherence, which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. Here we review recent advances in optimal control methodology that allow typical tasks in device operation for open quantum systems to be tackled and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions.
This paper presents an adaptive quantum decoherence control theory based on feedback control. The core claim is to develop a precise method for controlling the interaction between a quantum system and its environment, ultimately achieving prolonged quantum state preservation. The proposed theory utilizes a dynamic model of the quantum system coupled with its environment and employs a feedback control algorithm to adjust control parameters in real-time, effectively mitigating decoherence effects. The novelty lies in the application of feedback control methodologies to quantum systems, offering a new approach to quantum state maintenance. The theoretical framework is detailed, focusing on the mathematical formulation of the control problem and the design of the adaptive control strategy. We introduce a novel approach to quantifying and addressing decoherence, moving beyond traditional static control methods by incorporating real-time environmental feedback. The presented adaptive control scheme promises enhanced robustness and precision in manipulating quantum states, particularly in environments with fluctuating decoherence rates. The paper concludes with a discussion of potential applications and future research directions.
Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of problems, has limited capabilities, e.g., if the initial and desired target states have density matrices with different spectra or if a control field needs to be designed to optimally transfer different initial states to the same target state. Recent research works suggest extending coherent control by including active manipulation of the non-unitary (i.e., incoherent) part of the evolution. This paper summarizes recent results specifically for incoherent control by the environment (e.g., incoherent radiation or a gaseous medium) with a kinematic description of controllability and landscape analysis.
Coherence control was originally conceived by Shapiro and Brumer for closed quantum systems. In open quantum systems, the environment hampers or destroys coherence. Nevertheless, the Kurizki-Shapiro-Brumer coherent photocurrent control showed partial resilience to decoherence. Still, decoherence control is an essential prerequisite to our ability to fully exploit quantum coherence for any operational task. Yet decoherence control need not employ coherent fields: it may be incoherent. In operational tasks such as the preparation, transformation, transmission, and detection of quantumstates, environmental (bath) effects can be suppressed by dynamical decoupling, or by the more general incoherent dynamical control by modulation developed by our group. The resulting control dynamics must be Zeno-like in order to yield suppressed coupling to the bath in unitary operational tasks. There are however tasks which cannot be implemented by closed-system (unitary) evolution, in particular those involving a change of the system's entropy. Such tasks necessitate efficient coupling to a bath for their implementation. Examples are the use of measurements to cool (purify) a system, to equilibrate it, or harvest (and convert) energy from the environment. If the underlying dynamics is anti-Zeno like, enhancement of this coupling to the bath will occur and thereby facilitate the task, as discovered by us. A general task may also require state and energy transfer between non-interacting parties via shared modes of the bath. For such tasks, a more subtle interplay of Zeno and anti-Zeno dynamics may be optimal. We have therefore constructed a general framework for optimizing the way a system interacts with its environment to achieve a desired task. This optimization consists in adjusting a given “score” that quantifies the success of the task, such as the targeted fidelity, purity, entropy, energy or state transfer probability by dynamical modification of the system-bath coupling spectrum on demand.
This paper explores the application of quantum decoherence control to optimize complex systems. Traditional optimization methods often struggle with the inherent complexity and dynamic nature of systems such as supply chains and transportation networks. We propose a novel approach leveraging the principles of quantum decoherence. Specifically, we introduce the concept of "decoherence interventions," strategically applied during system operation to manipulate parameters and mitigate negative impacts, ultimately leading to dynamic optimization. The core idea is to exploit the controllable nature of decoherence – a fundamental quantum phenomenon – to achieve a level of precision not attainable with classical methods. This work lays the groundwork for a new paradigm in optimization, potentially unlocking significant improvements in system performance and resilience. The theoretical framework presented provides a foundation for future research exploring the practical implementation and scalability of this technique. We present a mathematical model demonstrating the core principles and illustrate the potential for adaptive control strategies.
Known as decoherence, the unavoidable interaction of a quantum system with its surrounding environment is usually considered to be detrimental for quantum information processing. In this thesis the coherent, open loop control of such open systems is studied. Concepts from quantum control theory and the theory of open quantum system are adopted in order to fight decoherence and implement quantum gates in a noiseless manner. In particular, Lie algebraic methods and numerical optimization tools are used to investigate the control properties of a single spin interacting with a spin environment. We show that, independent of the size of the environment, every unitary transformation can be implemented on the system spin through a single control field. We proceed by investigating dynamical decoupling, a method to suppress the interactions with the environment, for finite- and for in- finite dimensional systems. We prove that every finite dimensional system can be protected from decoherence, even if the environment is infinite dimensional, whereas for noise described by a Lindblad master equation dynamical decoupling will never succeed. This will lead to a new method to distinguish decoherence from intrinsic noise terms. We further prove that not every infinite dimensional system can be protected from decoherence through dynamical decoupling. Afterwards we investigate dynamical decoupling of systems that are described by quadratic Hamiltonians, showing that such interactions can always be suppressed with two simple operations. In the last part we investigate the coherent control of a Lindblad master equation. We show that a strong noise process exhibiting a decoherence free subspace can substantially increase the number of unitary operations that can be implemented, allowing us to fully control parts of the system. Afterwards we develop a scheme to make Hamiltonians and Lindbladians commutative by adding an auxiliary system. The old, possibly non-commutative dynamics, is recovered through a non-selective measurement.