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Chinese Control Conference (CCC)

Noise Decoupling Decoherence Suppression Strategy for Markov Open Quantum Systems

Jing Zhang, Jianyong Li, Jianwu Wu

Published Aug 1, 2006• 1 citation
Publisher

Abstract

The problem of decoherence suppression for the general N-level Markov open quantum systems is studied. Here, the quantum feedback control strategy is presented for the quantum ensemble. In order to find the control Hamiltonians and the measured observables, the new concept of the noise decoupling decomposition for the su(N) Lie algebra is introduced. It is shown that some state variables of the coherence vector of the system density matrix can be completely decoupled from the environmental noises under the feedback control.

DOI
10.1109/chicc.2006.280931

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The problem of decoherence suppression for the general N-level Markov open quantum systems is studied. Here, the quantum feedback control strategy is presented for the quantum ensemble. In order to find the control Hamiltonians and the measured observables, the new concept of the noise decoupling decomposition for the su(N) Lie algebra is introduced. It is shown that some state variables of the coherence vector of the system density matrix can be completely decoupled from the environmental noises under the feedback control.
The noise decoupling problem is investigated for general NNN-level Markovian open quantum systems. First, the concept of Cartan decomposition of the Lie algebra su(N)\mathrm{su}(N)su(N) is introduced as a tool of designing control Hamiltonians. Next, under certain assumptions, it is shown that a part of variables of the coherence vector of the system density matrix can be asymptotically decoupled from the environmental noises. The resulting noise decoupling scheme is applied to one-qubit, qutrit, and two-qubit quantum systems, by which the coherence evolution of the one-qubit and qutrit systems can always be asymptotically preserved, while, for two-qubit systems, our findings indicate that evolution of some variables can be preserved only for some initial states.
The decoherence suppression issue is studied for two-level quantum systems based on coherent control strategy.The model of two-level open quantum systems under coherent control is formulated,in which the decoherence suppression is equivalent to the decoupling problem of the system from environmental noises.Then,an open-loop control is designed to suppress decoherence,which is shown to be capable of asymptotically decoupling a part of the dynamic variables of the system from the environmental noises.Finally,feedback control strategy is introduced so that the corresponding state variables can be precisely decoupled form the environmental noises without being affected by the noises induced by quantum measurement in feedback control.
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.
Since there are many examples in which no decoherence-free subsystems exist (among them all cases where the error generators act irreducibly on the system Hilbert space), it is of interest to search for novel mechanisms which suppress decoherence in these more general cases. Drawing on recent work (quant-ph/0502153) we present three results which indicate decoherence suppression without the need for noiseless subsystems. There is a certain trade-off; our results do not necessarily apply to an arbitrary initial density matrix or for completely generic noise parameters. On the other hand, our computational methods are novel and the result---suppression of decoherence in the error-algebra approach without noiseless subsystems---is an interesting new direction.
Dynamical decoupling as a quantum control strategy aims at suppressing quantum decoherence adopting the popular philosophy that the disorder in the unitary evolution of the open quantum system caused by environmental noises should be neutralized by a sequence of ordered or well-designed external operations acting on the system. This work studies the solution of quantum-state-diffusion equations by mixing two channels of environmental noises, i.e., relaxation (dissipation) and dephasing. It is interesting to find in two-level and three-level atomic systems that a non-Markovian relaxation or dissipation process can be suppressed by a Markovian dephasing noise. The discovery results in an anomalous control strategy by coordinating relaxation and dephasing processes. Our approach opens an avenue of noise control strategy with no artificial manipulation over the open quantum systems.
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.