%0 Journal Article
%T Fast and virtually exact quantum gate generation in U ( n ) via iterative Lyapunov methods
%+ Polytechnic School of the University of São Paulo (Brazil)
%+ Department of Automation and Systems (DAS)
%+ Centre Automatique et Systèmes (CAS)
%+ QUANTum Information Circuits (QUANTIC)
%A Pereira Da Silva, Paulo Sergio
%A Silveira, Hector Bessa
%A Rouchon, Pierre
%< avec comité de lecture
%@ 0020-7179
%J International Journal of Control
%I Taylor & Francis
%V 00
%P 1-15
%8 2019-06-13
%D 2019
%R 10.1080/00207179.2019.1626023
%K controllability
%K quantum control
%K right-invariant systems
%K Lyapunov stability
%K quantum gates
%Z Engineering Sciences [physics]/Automatic
%Z Physics [physics]/Quantum Physics [quant-ph]Journal articles
%X A new approach for quantum gate generation, called Reference Input Generation Algorithm (RIGA) is introduced. Let X −1 (t) be the trajectory that is obtained in step − 1, with X −1 (t) = I. In step , X −1 is right-translated in order to displace X −1 (T f) to X goal. The translated trajectory is used as a reference for a Lyapunov-based tracking control law, generating X (t) and so on. A proof of the exponential convergence of X −1 (T f) to zero is provided for T f large enough. Two examples presents numerical experiments regarding N coupled qubits. The first example considers N = 3 with a known minimum time T *. It presents excellent results for T f ≤ T *. The second example is a benchmark for the comparison between RIGA and GRAPE, considering a Hadamard gate for the systems with N = 2, 3,. .. , 10 qubits. The runtime of RIGA could be improved, and GRAPE was implemented in a faster CPU. However, RIGA presents results that are similar to GRAPE, with faster runtime in some cases, showing that the RIGA is indeed a promising algorithm.
%G English
%L hal-02289258
%U https://hal-mines-paristech.archives-ouvertes.fr/hal-02289258
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