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Dissertation
Control of Open Quantum Systems: Examples & Methods for Non-Markovian Dynamics
(2023)
Usually open quantum systems are considered to be under the influence of noise and therefore faulty. On the other hand, a controlled system is regarded as something stable and predictable. It is often neglected, that the two aspects are very closely related. A perfectly isolated quantum system will not be subject to environmental influences, but this makes it also impossible to interact with it in any manner. Controlling and measuring such a system is impossible and therefore of no technical relevance. Every system ...
Aufsatz
Optimal control theory for a unitary operation under dissipative evolution
(2014)
We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: the target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish ...
Aufsatz
Hybrid optimization schemes for quantum control
(Springer Open, 2015)
Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized ...
Aufsatz
Exploiting non-Markovianity for quantum control
(Nature Publishing Group, 2015)
Quantum technology, exploiting entanglement and the wave nature of matter, relies on the ability to accurately control quantum systems. Quantum control is often compromised by the interaction of the system with its environment since this causes loss of amplitude and phase. However, when the dynamics of the open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Interaction with the environment is then not necessarily detrimental. We show that the ...
Aufsatz
Beating the limits with initial correlations
(2017-11-28)
Fast and reliable reset of a qubit is a key prerequisite for any quantum technology. For real world open quantum systems undergoing non-Markovian dynamics, reset implies not only purification, but in particular erasure of initial correlations between qubit and environment. Here, we derive optimal reset protocols using a combination of geometric and numerical control theory. For factorizing initial states, we find a lower limit for the entropy reduction of the qubit as well as a speed limit. The time-optimal solution ...
Dissertation
Optimal Control of Quantum Information Tasks in Open Quantum Systems
(2020-07-30)
Every quantum system inevitably interacts with its environment. This is a fundamental requirement that allows us to control, measure and, in general, interact with quantum systems. In that respect, a quantum system's openness can be interpreted as prerequisite that enables quantum technologies in the first place. The latter are built to harness the intrinsic quantum mechanical behavior of quantum devices in order to build new, powerful technologies. However, a quantum system's openness also causes it to interact ...
Dissertation
Quantum optimal control theory of photoelectron spectroscopy
(2018)
The object of this doctoral thesis is two-fold and can be classified into two, but intrinsically related categories: (i) development of theoretical models for the simulation of electron dynamics and in parallel to this, (ii) method development of efficient numerical algorithms for ad hoc control of photoelectron and photoion-related observables. The first category primarily focuses on the development of a variety of theoretical models describing the interaction of light and matter for the extraction and control of ...
Aufsatz
Controlling the transport of an ion: classical and quantum mechanical solutions
(IOP, 2014)
The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant ...
Dissertation
Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications
(2015-06-19)
Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence.
In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on ...
Dissertation
Optimizing Robust Quantum Gates in Open Quantum Systems
(2015-05-27)
We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum ...