The application of coherent interactions in a controllable manner in order to guide the dynamics of quantum systems is usually termed Quantum Control. During the early stages of the field, and in m...
The rapid growth of quantum information sciences over the past few decades has fueled a corresponding rise in high profile applications in fields such as metrology, sensors, spintronics, and attosecond dynamics, in addition to quantum information processing. Realizing this potential of today's quantum science and the novel technologies based on this requires a high degree of coherent control of quantum systems. While early efforts in systematizing methods for high fidelity quantum control focused on isolated or closed quantum systems, recent advances in experimental design, measurement and monitoring, have stimulated both need and interest in the control of complex or large scale quantum systems that may also be coupled to an interactive environment or reservoir. This focus issue brings together new theoretical and experimental work addressing the formulation and implementation of quantum control for a broad range of applications in quantum science and technology today.
Quantum mechanics, though a probabilistic theory, gives a 'deterministic' answer to the question of how the present determines the future. In essence, in order to predict future probabilities, we need to (numerically) propagate the time-dependent Schrödinger equation from the present to the future. It is interesting to note that classical mechanics of macroscopic bodies, though reputed to be a deterministic theory, does not allow, due to chaos (which unfortunately is more prevalent than integrability), such clear insights into the future. In contrast, small (e.g., atomic, molecular and photonic) systems which are best understood using the tools of quantum mechanics, do not suffer from chaos, rendering the prediction of the probability-distributions of future events possible. The field of quantum control deals with an important modification of this task, namely, it asks: given a wave function in the present, what dynamics, i.e. what Hamiltonian, guarantees a desired outcome or 'objective' in the future? In practice one may achieve this goal of modifying and finding the desired Hamiltonian by introducing external fields, e.g. laser light. It is then possible to reach the objective in a 'trial-and-error' fashion, performed either numerically or in the laboratory. We can guess or build a Hamiltonian, do an experiment, or propagate the initial wave function to the future, compare the result with the desirable objective, and correct the guess for the Hamiltonian until satisfactory agreement with the objective is reached. A systematic way of executing this procedure is the sub-field called 'optimal control'. The trial-and-error method is often very time consuming and rarely provides mechanistic insight. There are situations where analytical solutions exist, rendering the control strategies more transparent. This is especially so when one can identify quantum interferences as the heart of quantum control, the essence of the field called 'coherent control'. The experience accumulated so far by many groups is that quantum interferences are the mechanism underlying most successful control scenarios and control experiments. The identification of the control mechanism is especially facile when the time-dependence of the Hamiltonian merely serves to prepare a state which then evolves in the absence of external fields. Analytical theories also exist when the explicit time dependence of the Hamiltonian can be treated adiabatically. Under these circumstances one can identify the quantum interfering pathways that lead to control, allowing for the simultaneous exploration of entire 'landscapes' (and not just a single 'desirable' objective) resulting from varying all the experimental 'knobs' at our disposal, e.g., relative- and envelope-phases, intensities, polarizations, and pulse-sequencing. Such 'pulse-shaping' knobs are now available down to the sub-femtosecond regime in broad spectral regions ranging from the UV to the IR. We expect that comprehensive investigations of the quantum interference required to control dynamical processes will result in a more detailed understanding of the dynamics themselves. Together with experimental progress---the stage is now set for many exciting applications in fundamental and applied sciences by 'tailoring' light--matter interactions essentially at will.
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 recently emerged field of quantum technology is aiming to employ quantum coherence and entanglement for realization of next generation sensors, standards, imaging systems, secure communication and computers.Although applications of quantum technologies cover a broad spectrum and their development stage varies from early demonstrations to commercially available devices, many challenges have been identified.The first includes tailoring materials for quantum technologies, which is playing an essential role in technological applications of quantum science.Solid state systems allowing long coherence time are essential for quantum computation and quantum sensing.Ultrapure materials with tailored isotopic content are important for reaching long coherence time of spin qubits (Awschalom et al., 2013).The ability to place single dopants with high precision and form spin qubits at desired location is essential for both quantum computing and quantum sensing applications (McCallum et al., 2012;Smith et al., 2019).The performance of different types of qubits is usually benchmarked in terms of controllability and coherence time.Usually solid-state systems allow fast control, but exhibit fast decoherence owing to complex environment.It is therefore important to search for new types of qubits combining isolation from environment and access via fast coherent control and readout.Novel approaches combining different quantum systems into build hybrid quantum devices for optimal performance is a promising avenue.Examples of such hybrid approaches are spin systems coupled to superconducting qubits (Kubo et al., 2011) and hybrid nuclear-electronic qubits (Morley et al., 2013).Optimal protocols for quantum technologies requires extension of coherence time of qubits beyond the coherence time of the isolated quantum system.The efficient protection toolkit includes dynamical decoupling (Yang et al., 2011) and quantum error correction (Terhal, 2015) based techniques.Although general principles of qubits protection were developed and tested experimentally in different model environments, it is essential to adapt them to realistic environmental noise.In the field of quantum sensing, it is also essential to combine protections against noise with non-reduced sensing performance.Experimental imperfections can be addressed using optimal control tools (Glaser et al., 2015).The development of efficient quantum algorithms is another growing field belonging to quantum software area.On one hand, it is essential to find problems where a quantum computer can outperform classical computers.On the other hand, it is essential to develop an application scenario for a limited number of qubits (Montanaro, 2016).In addition, in order to develop new algorithms, future work must include discoveries of application scenarios of already known algorithms.Application of quantum Fourier transform for sensing is a promising example of such new applications (Vorobyov et al., 2021).Signal processing is another field of quantum software that is becoming essential in applications.Advanced signal analysis protocols, like quantum compressed sensing, can be employed to quantify entanglement in large quantum devices via efficient quantum tomography (Riofrío et al., 2017).