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.
Highlights
Controlling quantum dynamics may provide access to efficiently performing computational tasks or to simulating the behaviour of other quantum systems that are beyond experimental handling themselves
As has been experimentally demonstrated by NMR [14,15], these algorithms can be implemented using thermal mixtures of quantum states. It suffices to approximate the trace of a controlled unitary encapsulating the information of the Jones polynomial. This class of quantum algorithms is equivalent to deterministic quantum computation with one clean qubit (DQC1) [16], and it is even DQC1-complete [17,18], where general belief has it that P DQC1 BQP (e.g. Shor & Jordan [17])
We will illustrate how thermal ensembles can be used for approximating the trace of a unitary matrix [80]. This paves the way to a recent class of quantum algorithms related to the knot theory, because it allows for efficiently evaluating Jones polynomials over a range of parameters
Summary
Controlling quantum dynamics may provide access to efficiently performing computational tasks or to simulating the behaviour of other quantum systems that are beyond experimental handling themselves. Both quantum computation and simulation are challenging quantum engineering tasks requiring high-level manipulations of quantum dynamics To this end, among the mathematical tools [25,26] optimal control algorithms have been establishing themselves as indispensable [27,28]. Taking the concept of decoherence-free subspaces [56,57] to more realistic scenarios, avoiding decoherence in encoded subspaces [58] complements recent approaches of dynamic error correction [59,60] Along these lines, quantum control is anticipated to contribute significantly to bridging the gap between quantum principles demonstrated in pioneering experiments and high-end quantum.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
