The scaling of effort to achieve control objectives with system size is an important consideration in the development of many quantum devices, especially in those intended for quantum information processing. This thesis investigates the scaling with system size of effort required to control manybody quantum systems, and asks whether this is sufficiently favourable to enable supremacy in quantum computation. This is tested using quantum control theory and numerical control optimisation, which are well established tools for investigating the dynamics of driven quantum systems, in a variety of theoretical models related to state-of-the-art quantum devices. Gates acting on a chain of coupled oscillators are found to achievable in times that scale approximately linear with chain length, where the control is over only a single oscillator. The scalability of a scheme for implementing quantum gates in a many-body quantum simulator is shown to be favourable enough to allow for them to be configured to perform quantum computations. A state measurement protocol is proposed as part of the scheme. The scalability is validated through numerical simulation of simulator models composed of up to 9 qubits. The reachable set of operations for systems with quadratic Hamiltonians and infinite-dimensional Hilbert spaces is investigated. The passive operations in quantum optics are proven to be unreachable for single-mode systems with ‘unstable’ Hamiltonians. Further characterisation of the reachable set is made through numerical simulation of control optimisation. Some progress is made in extending the reachability result to n-modes. A non-Markovian noise model is used in simulating control optimisation of a dynamical decoupling scheme, which would be impossible to simulate with Markovian dynamics. The popular QuTiP Python library has been extended to allow simulation of control optimisation with a range of dynamical models. A description of these software modules and their method of use is given. Many of the software tools developed for the study are made available through open-source repositories. Some outlook is given for the use of in-situ open-loop control in optimising controls in quantum system experiments.
The scaling of effort to achieve control objectives with system size is an important consideration in the development of many quantum devices, especially in those intended for quantum information processing. This thesis investigates the scaling with system size of effort required to control manybody quantum systems, and asks whether this is sufficiently favourable to enable supremacy in quantum computation. This is tested using quantum control theory and numerical control optimisation, which are well established tools for investigating the dynamics of driven quantum systems, in a variety of theoretical models related to state-of-the-art quantum devices. Gates acting on a chain of coupled oscillators are found to achievable in times that scale approximately linear with chain length, where the control is over only a single oscillator. The scalability of a scheme for implementing quantum gates in a many-body quantum simulator is shown to be favourable enough to allow for them to be configured to perform quantum computations. A state measurement protocol is proposed as part of the scheme. The scalability is validated through numerical simulation of simulator models composed of up to 9 qubits. The reachable set of operations for systems with quadratic Hamiltonians and infinite-dimensional Hilbert spaces is investigated. The passive operations in quantum optics are proven to be unreachable for single-mode systems with ‘unstable’ Hamiltonians. Further characterisation of the reachable set is made through numerical simulation of control optimisation. Some progress is made in extending the reachability result to n-modes. A non-Markovian noise model is used in simulating control optimisation of a dynamical decoupling scheme, which would be impossible to simulate with Markovian dynamics. The popular QuTiP Python library has been extended to allow simulation of control optimisation with a range of dynamical models. A description of these software modules and their method of use is given. Many of the software tools developed for the study are made available through open-source repositories. Some outlook is given for the use of in-situ open-loop control in optimising controls in quantum system experiments.
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 the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.
The study of open quantum systems forms one of the main problems of modern physics. This thesis aims at contributing to this field, and focuses on the investigation of non-Markovian dynamics of open quantum systems. Here, as a special case, quantum many-body systems provide for a rich field of research. With the ability to control them being of essential importance for the development of quantum technologies, the characterization of their dynamical properties has also drawn a lot of interest lately. One of the main methodological tasks in the study of open quantum systems is to reduce the infinite degrees of freedom of the total system. In order to achieve this, the thesis makes use of the tensor network method matrix product states and combines it with the picture of the quantum stochastic Schrödinger equation. However, when computing the dynamics of many-body systems of system size N, even the reduced system dynamics scale with 2N, making larger system sizes difficult to access. Therefore, especially when computing non-Markovian time-dynamics where the information backflow from the reservoir has to be taken into account, efficiently constructed algorithms are required. This thesis proposes these type of algorithms and demonstrates their application. They enable an access to larger system sizes, thus making it possible to investigate non-equilibrium steady-states of quantum many-body systems in a non-Markovian interaction for system sizes up to N=30. This thesis consists of three parts. The first part provides an introduction to the theory of open quantum systems and to the methodology for modeling them. The second part examines many-body system-reservoir interaction in the non-Markovian regime by investigating the case of fully coherent self-feedback. It uses the one-dimensional Heisenberg spin-1/2 chain as a paradigmatic and recently intensely studied many-body system. It is demonstrated that this gives rise to new conditions for the feedback phase and to highly non-trivial states within the system as well as to the possibility of partially characterizing the system non-invasively and storing excitation within it. Next, a novel approach to the boundary-driven Heisenberg chain is presented, where the chain is exposed to a coherent driving field, thus enabling a comparison to the well-studied incoherently driven model. The third part demonstrates the use of an external pump to control the feedback phase of a Lambda-type three-level system, where the external pump pulse is shown to be a new control parameter. The thesis concludes with the proposition to enhance the indistinguishability of two photons by feedback control.
Simulating quantum many-body systems is essential for understanding complex phenomena in condensed matter, chemistry, and materials science. Quantum computing offers a way to overcome the limitations of classical methods by operating directly in exponentially large Hilbert spaces. In particular, classical methods often fail to capture the dynamics of strongly correlated systems, which makes quantum algorithms a promising alternative for exploring these challenging regimes. This thesis uses quantum dynamics simulations to probe the behaviour of many-body systems. We first introduce a spectroscopy-based protocol to extract excitation spectra from the time evolution of observables and analyse its performance on near-term quantum devices. We show that the protocol requires only short evolution times and is resilient to errors, facilitating its implementation on real hardware. Building on this, we simulate fermionic excitation spectra using current quantum devices, introducing resource optimisations - including an approximate free-fermion initial state, a unitary quench without ancillae, and reduced Trotter steps - that significantly lower circuit depth. These improvements enable simulations at system sizes competitive with the state of the art, yielding results that match classical benchmarks. While most studies focus on unitary dynamics of isolated systems, open quantum dynamics is increasingly relevant for describing non-equilibrium processes across biology, materials science, and quantum control. We extend our scope to systems coupled to an environment and governed by Lindbladian evolution. By studying simulation complexity through physically meaningful quantities - such as correlation length and mixing time - we explore whether open-system dynamics can be as tractable as their unitary counterparts. These findings provide insights into the computational complexity landscape of open-system simulation and highlight regimes where quantum methods offer a clear advantage.
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.
Quantum communication provides essentially secure transmission of information and quantum sensing provides measurement sensitivities better than classical. These powers come because of unique quantum processes, especially superposition and entanglement. Although there is a significant theoretical and experimental development, the phenomenon of decoherence is still one of the main limiting factors in performance and scalability of quantum devices. The importance of this study is that it considers an active approach to decoherence as one of the key impediments to scalable quantum technologies. Although the research on the noise sources and error mechanisms has been done extensively, the characterization is not enough to be applied to the real world. This study makes use of a theoretical and computation effort to explore scalable quantum technologies integrated decoherence control strategies. The research paper is based on the open quantum systems framework, in which quantum systems are represented as finite-dimensional systems that interact with the external environment. The findings of the study highlight that active decoherence control plays an important role in enhancing performance of open quantum systems. Without any control, the simulated quantum system is characterized by a fast decoherence time, coherence times are short, about 20 u ms, and the physical error rate is about 2.5%. The hybrid strategy is a feasible way to achieve fault-tolerant quantum operation and the transition point between theory-based control architectures and experimental hardware limitations, thus speeding up the development of reliable large-scale quantum technologies. The findings affirm that each of the isolated methods like dynamical decoupling, quantum error correction, or reservoir engineering can only be a partial solution when used alone. Adaptive and real-time control schemes responding dynamically to changing noise environments also require further research to develop them.
Quantum chaos concerns the emergence of universal statistical and dynamical prop- erties in quantum systems whose classical counterparts exhibit chaotic behavior. Unlike classical chaos, which can be characterized by sensitivity to initial conditions and exponential divergence of trajectories, quantum chaos manifests itself through a variety of indirect diagnostics, including spectral correlations, operator growth, and information scrambling. Understanding how these signatures arise from microscopic dynamics, and how they can be accessed in realistic many-body systems, is a central challenge in modern physics. This thesis investigates quantum chaos from complementary theoretical and practical perspectives. On the theoretical side, it develops effective descriptions of chaotic dy- namics in many-body systems with approximate symmetries, focusing on how weak symmetry breaking controls the exploration of Hilbert space and the crossover to random-matrix universality. Using perturbative arguments, numerical simulations, and a nonlinear sigma-model formulation, we identify a regime of Hilbert-space dif- fusion in which chaotic dynamics unfolds through a slow, collective spreading across nearly decoupled symmetry sectors. On the practical side, the thesis addresses the question of how paradigmatic chaotic models can be realized and probed in controlled experimental platforms. In partic- ular, it explores quantum simulation schemes for Sachdev–Ye–Kitaev (SYK) models using cavity quantum electrodynamics. By employing time-dependent disorder and Trotterized evolution in single-mode optical cavities, we demonstrate how low-rank interactions can be systematically promoted to effective all-to-all randomness, re- producing the spectral and dynamical signatures of SYK physics. Extensions to open-system dynamics are discussed, including Lindbladian realizations and the role of dissipation. The thesis thus highlights the connections between effective descriptions of quantum chaos and their implementation in controlled quantum simulation settings.