Related papers: Employing Typicality in Optimal Control Theory
Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic…
We discuss a quantum typicality approach to examine systems composed of two subsystems at different temperatures. While dynamical quantum typicality is usually used to simulate high-temperature dynamics, we also investigate low-temperature…
Quantum supremacy is the ability of quantum processors to outperform classical computers at certain tasks. In digital random quantum circuit approaches for supremacy, the output distribution produced is described by the Porter-Thomas (PT)…
Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the…
Designing cooling protocols is believed to require knowledge of the system spectrum. In contrast, cooling in nature occurs whenever the system is coupled to a cold bath. How does nature know how to cool? A natural cold bath can be mimicked…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
Quantum typicality refers to the phenomenon that the expectation values of any given observable are nearly identical for the overwhelming majority of all normalized vectors in a sufficiently high-dimensional Hilbert (sub-)space. As a…
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum…
Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of…
Optimal control theory is developed for the task of obtaining a primary objective in a subspace of the Hilbert space while avoiding other subspaces of the Hilbert space. The primary objective can be a state-to-state transition or a unitary…
Control of open quantum systems is an essential ingredient to the realization of contemporary quantum science and technology. We demonstrate such control by employing a thermodynamically consistent framework, taking into account the fact…
The development of quantum control methods is an essential task for emerging quantum technologies. In general, the process of optimizing quantum controls scales very unfavorably in system size due to the exponential growth of the Hilbert…
Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems…
Tremendous research efforts have been invested in exploring and designing so-called shortcuts to adiabaticity. These are finite-time processes that produce the same final states that would result from infinitely slow driving. Most of these…
We study the application of a generalized form of the level set method used in classical physical contexts to quantum optimal control situations. The set of OCT equations needed to keep the expectation value of an observable constant is…
Cooling of a quantum system is limited by the size of the control forces that are available (the "speed" of control). We consider the most general cooling process, albeit restricted to the regime in which the thermodynamics of the system is…
The extraordinary success in laser cooling, trapping, and coherent manipulation of atoms has energized the efforts in extending this exquisite control to molecules. Not only are molecules ubiquitous in nature, but the control of their…
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing…
Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different…
We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal…