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Control of open quantum systems: Case study of the central spin model

Christian Arenz, Giulia Gualdi, Daniel Klaus Burgarth

Published Aug 15, 2016• 24 citations
OpenAlex

Abstract

Abstract. We study the controllability of a central spin guided by a classical field and interacting with a spin bath, showing that the central spin is fully controllable independently of the number of bath spins. Additionally we find that for unequal system-bath couplings even the bath becomes controllable by acting on the central spin alone. We then analyze numerically how the time to implement gates on the central spin scales with the number of bath spins and conjecture that for equal system-bath couplings it reaches a saturation value. We provide evidence that sometimes noise can be effectively suppressed through control. 1.

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Control of open quantum systems: case study of the central spin model

Christian Arenz, Giulia Gualdi, Daniel Klaus Burgarth

We study the controllability of a central spin guided by a classical field and interacting with a spin bath and show that the central spin is fully controllable independently of the number of bath spins. Additionally we find that for unequal system-bath couplings even the bath becomes controllable by acting on the central spin alone. We then analyze numerically how the time to implement gates on the central spin scales with the number of bath spins and conjecture that for equal system-bath couplings it reaches a saturation value. We provide evidence that sometimes noise can be effectively suppressed through control.

arXiv:1312.0160•New Journal of Physics•Jun 26, 2014•39 citations

Decoherence and control of a qubit in spin baths: an exact master equation study

Jun Jing, Lian-Ao Wu

In spin-based nanosystems for quantum information processing, electron spin qubits are subject to decoherence due to their interactions with nuclear spin environments. In this paper, we present an exact master equation for a central spin-1/2 system in time-dependent external fields and coupled to a spin-half bath in terms of hyperfine interaction. The master equation provides a unified description for free and controlled dynamics of the central spin and is formally independent of the details and size of spin environments. Different from the previous approaches, the master equation remains exact even in the presence of external control fields. Using the parameters for realistic nanosystems with nonzero nuclear spins, such as GaAs, we investigate the Overhauser's effect on the decoherence dynamics of the central spin under different distributions of bath-spin frequencies and system-bath coupling strengths. Furthermore, we apply the leakage elimination operator, in a nonperturbative manner, to this system to suppress the decoherence induced by hyperfine interaction.

Scientific Reports•Jan 18, 2018•31 citations

Dynamics and control of a qubit in spin environment: an exact master equation study

Jun Jing, Lian-Ao Wu

We present an exact master equation for a central spin-$1/2$ system coupled to a spin-$1/2$ bath in terms of hyperfine interaction, which provides a unified formalism for both free evolution and controlled dynamics of the central spin. The equation enables us to study controllability of dynamics processes with various degrees of non-Markovianity. We investigate the Overhauser's effect on decoherence dynamics of the central spin under different bath spectra and the system-bath coupling strengths. Nonperturbative leakage elimination approach is applied to the system to suppress decoherence in solid-state quantum information processing.

arXiv:1601.07197•Jan 26, 2016•0 citations

Control of Open Quantum Systems

Christian

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.

•Mar 20, 2026•0 citations

Central spin models: Quantum integrability andhyperfine induced spin dynamics

B. Erbe

The spin degree of freedom has become subject to one of the broadest and most intensively studied fields of research in physics. The present thesis is part of this field and deals with so-called central spin models. The thesis is devided into two parts. In the first one we investigate very basic properties of central spin models on an abstract level. We introduce a new, or rather enhanced, notion of quantum integrability. From this we derive an explicit and, to a certain extent, analytical relation between integrability and decoherence. Then we specify a model of two coupled Gaudin models with all coupling constants being equal to each other (``homogeneous''). We numerically study the spectral properties of the model and find the spectrum to exhibit systematically degenerate multiplets. We briefly discuss possible applications in solid state quantum information processing. The second part is devoted to concrete physical considerations in the context of solid state quantum information processing. Here we consider two exchange coupled electron spins confined in semiconductor quantum dots and evaluate the hyperfine induced spin dynamics for the case of a weak magnetic field applied to the electron spins by exact methods. In a first step we consider the two exchange coupled electron spins to interact with the same bath of nuclear spins via homogeneous couplings. In particular we derive a scaling law for the decoherence time. In a second step we try to turn vice into virtue by investigating to what extent it is possible to swap and entangle two separate nuclear spin baths. Surprisingly, it turns out that a nuclear swap is possible for weakly coupled nuclear spin baths of realistic size, but not for smaller ones. We indicate that under the same circumstances it should also be possible to fully entangle the baths. We close the thesis with a summary and an outlook on further important questions.

•Aug 16, 2011•0 citations

Optimal control of a spin bath

Lihong Dong, Hang Liang, Chang‐Kui Duan +4 more

Harnessing the dynamics of a microscopic system lies at the core of quantum information processing. For quantum systems with a small number of spins, optimal control has been shown to be an efficient method to realize high-fidelity quantum control. As the number of the spins increases, it becomes challenging to steer the dynamics of the quantum system due to the exponentially increasing dimension of Hilbert space. Herein, we propose a method to realize optimal control of a spin bath consisting of hundreds of spins. A central spin is used to monitor the dynamics of the spin bath under a control Hamiltonian. The information obtained from the central spin is fed back to the control Hamilton to realize optimal control over the spin bath. We take a nitrogen vacancy (NV) center in diamond as an example, and our numerical simulation shows that the dephasing time of the NV center can be improved by more than 2 orders of magnitude. Furthermore, our method is compatible with dc magnetometry, whose sensitivity can be improved by an order of magnitude compared to conventional Ramsey interference. Our method is also feasible for various other spin-based systems, such as quantum dots, phosphorus-doped silicon, and defects in silicon carbide.

Physical Review A•Jan 22, 2019•18 citations
Abstract. We study the controllability of a central spin guided by a classical field and interacting with a spin bath, showing that the central spin is fully controllable independently of the number of bath spins. Additionally we find that for unequal system-bath couplings even the bath becomes controllable by acting on the central spin alone. We then analyze numerically how the time to implement gates on the central spin scales with the number of bath spins and conjecture that for equal system-bath couplings it reaches a saturation value. We provide evidence that sometimes noise can be effectively suppressed through control. 1.
We study the controllability of a central spin guided by a classical field and interacting with a spin bath and show that the central spin is fully controllable independently of the number of bath spins. Additionally we find that for unequal system-bath couplings even the bath becomes controllable by acting on the central spin alone. We then analyze numerically how the time to implement gates on the central spin scales with the number of bath spins and conjecture that for equal system-bath couplings it reaches a saturation value. We provide evidence that sometimes noise can be effectively suppressed through control.
In spin-based nanosystems for quantum information processing, electron spin qubits are subject to decoherence due to their interactions with nuclear spin environments. In this paper, we present an exact master equation for a central spin-1/2 system in time-dependent external fields and coupled to a spin-half bath in terms of hyperfine interaction. The master equation provides a unified description for free and controlled dynamics of the central spin and is formally independent of the details and size of spin environments. Different from the previous approaches, the master equation remains exact even in the presence of external control fields. Using the parameters for realistic nanosystems with nonzero nuclear spins, such as GaAs, we investigate the Overhauser's effect on the decoherence dynamics of the central spin under different distributions of bath-spin frequencies and system-bath coupling strengths. Furthermore, we apply the leakage elimination operator, in a nonperturbative manner, to this system to suppress the decoherence induced by hyperfine interaction.
We present an exact master equation for a central spin-1/21/21/2 system coupled to a spin-1/21/21/2 bath in terms of hyperfine interaction, which provides a unified formalism for both free evolution and controlled dynamics of the central spin. The equation enables us to study controllability of dynamics processes with various degrees of non-Markovianity. We investigate the Overhauser's effect on decoherence dynamics of the central spin under different bath spectra and the system-bath coupling strengths. Nonperturbative leakage elimination approach is applied to the system to suppress decoherence in solid-state quantum information processing.
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.
The spin degree of freedom has become subject to one of the broadest and most intensively studied fields of research in physics. The present thesis is part of this field and deals with so-called central spin models. The thesis is devided into two parts. In the first one we investigate very basic properties of central spin models on an abstract level. We introduce a new, or rather enhanced, notion of quantum integrability. From this we derive an explicit and, to a certain extent, analytical relation between integrability and decoherence. Then we specify a model of two coupled Gaudin models with all coupling constants being equal to each other (``homogeneous''). We numerically study the spectral properties of the model and find the spectrum to exhibit systematically degenerate multiplets. We briefly discuss possible applications in solid state quantum information processing. The second part is devoted to concrete physical considerations in the context of solid state quantum information processing. Here we consider two exchange coupled electron spins confined in semiconductor quantum dots and evaluate the hyperfine induced spin dynamics for the case of a weak magnetic field applied to the electron spins by exact methods. In a first step we consider the two exchange coupled electron spins to interact with the same bath of nuclear spins via homogeneous couplings. In particular we derive a scaling law for the decoherence time. In a second step we try to turn vice into virtue by investigating to what extent it is possible to swap and entangle two separate nuclear spin baths. Surprisingly, it turns out that a nuclear swap is possible for weakly coupled nuclear spin baths of realistic size, but not for smaller ones. We indicate that under the same circumstances it should also be possible to fully entangle the baths. We close the thesis with a summary and an outlook on further important questions.
Harnessing the dynamics of a microscopic system lies at the core of quantum information processing. For quantum systems with a small number of spins, optimal control has been shown to be an efficient method to realize high-fidelity quantum control. As the number of the spins increases, it becomes challenging to steer the dynamics of the quantum system due to the exponentially increasing dimension of Hilbert space. Herein, we propose a method to realize optimal control of a spin bath consisting of hundreds of spins. A central spin is used to monitor the dynamics of the spin bath under a control Hamiltonian. The information obtained from the central spin is fed back to the control Hamilton to realize optimal control over the spin bath. We take a nitrogen vacancy (NV) center in diamond as an example, and our numerical simulation shows that the dephasing time of the NV center can be improved by more than 2 orders of magnitude. Furthermore, our method is compatible with dc magnetometry, whose sensitivity can be improved by an order of magnitude compared to conventional Ramsey interference. Our method is also feasible for various other spin-based systems, such as quantum dots, phosphorus-doped silicon, and defects in silicon carbide.