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  2. Introduction
  3. Sliding mode control of quantum systems - IOPscience
  4. Coherent Control of Quantum Systems with Increasing Complexity

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Quantum Technology has been recognised as one of the most promising frontier technologies. Although great progress has already been made, a lot of fundamental research is still needed for this area to become mature enough to foster wider practical applications. Much research in this area can be formulated as quantum control problems. Quantum control theory is drawing wide attention with research in this regard involving controllability, optimal control, feedback control, etc.

Although a number of results on control design of single quantum systems have been presented, there are few results for the control analysis and synthesis of quantum ensembles. A quantum ensemble consists of a large number of single quantum systems.


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Quantum ensembles have wide applications in emerging quantum technology including quantum computation, long-distance quantum communication, and magnetic resonance imaging. Once the system is coupled, significant entanglement is generated between all modes. In other words, the spin bath model can simulate the Caldeira-Leggett model, but the opposite is not true.

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An example of natural system being coupled to a spin bath is a nitrogen-vacancy N-V center in diamonds. In this example, the color center is the system and the bath consists of carbon 13 C impurities which interact with the system via the magnetic dipole-dipole interaction. For open quantum systems where the bath has oscillations that are particularly fast, it is possible to average them out by looking at sufficiently large changes in time.

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This is possible because the average amplitude of fast oscillations over a large time scale is equal to the central value, which can always be chosen to be zero with a minor shift along the vertical axis. This method of simplifying problems is known as the secular approximation. Open quantum systems that do not have the Markovian property are generally much more difficult to solve.

This is largely due to the fact that the next state of a non-Markovian system is determined by each of its previous states, which rapidly increases the memory requirements to compute the evolution of the system.

Introduction

Currently, the methods of treating these systems employ what are known as projection operator techniques. One such derivation using the projection operator technique results in what is known as the Nakajima—Zwanzig equation. This derivation highlights the problem of the reduced dynamics being non-local in time:.

While the Nakajima-Zwanzig equation is an exact equation that holds for almost all open quantum systems and environments, it can be very difficult to solve.

This means that approximations generally need to be introduced to reduce the complexity of the problem into something more manageable. Other examples of valid approximations include the weak-coupling approximation and the single-coupling approximation. In some cases, the projection operator technique can be used to reduce the dependence of the system's next state on all of its previous states.

This method of approaching open quantum systems is known as the time-convolutionless projection operator technique, and it is used to generate master equations that are inherently local in time. Because these equations can neglect more of the history of the system, they are often easier to solve than things like the Nakajima-Zwanzig equation. Another approach emerges as an analogue of classical dissipation theory developed by Ryogo Kubo and Y. This approach is connected to hierarchical equations of motion which embed the density operator in a larger space of auxiliary operators such that a time local equation is obtained for the whole set and their memory is contained in the auxiliary operators.

From Wikipedia, the free encyclopedia. A quantum mechanical system that interacts with a quantum-mechanical environment. Bibcode : Entrp..

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Sliding mode control of quantum systems - IOPscience

This article contains quotations from this source, which is available under the Creative Commons Attribution 4. Petruccione The Theory of Open Quantum Systems. Oxford University Press. The Journal of Chemical Physics. Bibcode : JChPh. Caldeira and A. Also, quantum feedback control may consist of measurement based feedback control, in which the controller is a classical system governed by the laws of classical physics.

Coherent Control of Quantum Systems with Increasing Complexity

Alternatively, quantum feedback control may take the form of coherent feedback control in which the controller is a quantum system governed by the laws of quantum mechanics. In the area of open loop quantum control, questions of controllability along with optimal control and Lyapunov control methods are discussed. Skip to main content Skip to table of contents. Encyclopedia of Systems and Control Living Edition.

Contents Search. Control of Quantum Systems. Living reference work entry First Online: 10 October