Controlling the dynamics or measurement of quantum systems via the manipulation of external parameters is a most important phenomenon that lies at the heart of several fields including atomic and optical physics, molecular chemistry and quantum information. As quantum technologies have matured, a host of practical applications of quantum control have been realized in quantum optics, cavity QED, atomic spin ensembles, ion trapping, and Bose--Einstein condensation. As a result, quantum control theory is a rapidly growing research field.

The aim of this special issue is to give an idea of the present status of research in quantum control, and to stimulate further activity. The papers chosen cover a great variety of ideas in this field. To aid the reader, we have divided the papers into four broad sections: quantum filtering and feedback control; open-loop control; quantum information applications; optical and related applications. Of course there are many papers that cross the boundaries between the categories we have identified, so we encourage readers to peruse the whole issue. While some may quibble with our classification scheme, we think it will be useful, especially to those who are new to the area. In each section the papers are ordered by date of submission.

The first section is on quantum filtering and feedback control. Quantum filtering means determining estimates for some (or all) observables of the system from classical measurement results obtained gradually over time from the output of the quantum system. The conditioned quantum state is one way to generate such estimates. This filtering of the measurement results is useful for feedback control (also known as closed-loop control), because those estimates can be used as the basis for varying the external control parameters. This section begins with a review article (the one exception to the ordering of papers by submission date).

The second section is on open-loop control in the broad sense. This is concerned with how to drive a quantum system from an initial given state to a pre-determined target state. This includes the question of controllability: whether a controller can drive a quantum system to a desired state, for which the main tools are group theory and graph theory. Quantum optimal control is concerned with finding the best control fields (according to some cost function) to achieve the desired target for a controllable system. Coherent control is a particularly powerful method for guiding the state of a quantum system (typically a molecule) towards the target by applying semiclassical potentials and exploiting quantum interference effects. Another technique is learning control (which can be considered a kind of closed-loop control) in which the experiment is run many times, and each time the output from the sample is used to modify the control fields for the next (independently prepared) sample.

The third and fourth sections are devoted more to applications. The third section comprises applications of ideas and techniques from quantum control (primarily coherent control) to quantum information. These include new schemes for and novel analyses of quantum logic operations, quantum error correction, quantum communication, and quantum algorithms. Finally, the fourth section contains papers on optical or atom-optical (i.e. matter wave) implementations of quantum control ideas, and related applications such as tomography.

In closing, we take the opportunity to express our gratitude to the authors of the papers and to the reviewers, for their respective efforts in preparing and ensuring the high quality of the work and its presentation.