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Control Aspects of Quantum Computing Using Pure and Mixed States

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journal contribution
posted on 2013-12-06, 00:00 authored by Thomas Schulte-Herbrüggen, Raimund Marx, Amr Fahmy, Louis Kauffman, Samuel Lomonaco, Navin Khaneja, Steffen J. Glaser
Steering quantum dynamics such that the target states solve classically hard problems is tan- tamount 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 emphasise 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 characterising the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavitiy grids, ion traps, NV-centres in scenarios of closed as well as open quantum systems.


This work was supported in part by the eu programmes qap, q-essence, and the exchange with coquit, moreover by the Bavarian excellence network enb via the International Doctorate Programme of Excellence Quantum Computing, Control, and Communication (qccc) as well as by the Deutsche Forschungsgemeinschaft (dfg) in the collaborative research centre sfb 631 as well as the international research group suported via the grant schu 1374/2-1. AF thanks NIH GM47467.


Publisher Statement

This is a copy of an article published in the Philosophical Transactions A: Mathematical, Physical and Engineering Sciences © 2012 The Royal Society. DOI: 10.1098/rsta.2011.0513


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