title: Control aspects of quantum computing using pure and mixed states.
abstract: Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.
authors.affiliation: Department of Chemistry, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany. tosh@tum.de
authors.forename: Thomas
authors.initials: T
authors.lastname: Schulte-Herbrüggen
authors.forename: Raimund
authors.initials: R
authors.lastname: Marx
authors.forename: Amr
authors.initials: A
authors.lastname: Fahmy
authors.forename: Louis
authors.initials: L
authors.lastname: Kauffman
authors.forename: Samuel
authors.initials: S
authors.lastname: Lomonaco
authors.forename: Navin
authors.initials: N
authors.lastname: Khaneja
authors.forename: Steffen J
authors.initials: SJ
authors.lastname: Glaser
mesh_terms: D039301:Computers, Molecular / Q000639:trends*; D005246:Feedback; D016247:Information Storage and Retrieval / Q000639:trends*; D009682:Magnetic Resonance Spectroscopy / Q000379:methods*; D011789:Quantum Theory