https://hal-mines-paristech.archives-ouvertes.fr/hal-03500404Pereira da Silva, Paulo SergioPaulo SergioPereira da SilvaPolytechnic School of the University of São Paulo (Brazil) - USP - Universidade de São Paulo = University of São PauloRouchon, PierrePierreRouchonCAS - Centre Automatique et Systèmes - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettresQUANTIC - QUANTum Information Circuits - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettres - SU - Sorbonne Université - Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique - LPENS - Laboratoire de physique de l'ENS - ENS Paris - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité - Département de Physique de l'ENS-PSL - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettresSilveira, Hector BessaHector BessaSilveiraUFSC - Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis]A fixed point algorithm for improving fidelity of quantum gatesHAL CCSD2021ControllabilityQuantum controlRight-invariant systemsLyapunov stabilityBanach Fixed-Point Theorem[SPI.AUTO] Engineering Sciences [physics]/Automatic[PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]Chaplais, François2021-12-22 11:25:222023-01-13 03:41:192021-12-22 11:25:22enJournal articles10.1051/cocv/20200571This work considers the problem of quantum gate generation for controllable quantum systems with drift. It is assumed that an approximate solution called seed is pre-computed by some known algorithm. This work presents a method, called Fixed-Point Algorithm (FPA) that is able to improve arbitrarily the fidelity of the given seed. When the infidelity of the seed is small enough and the approximate solution is attractive in the context of a tracking control problem (that is verified with probability one, in some sense), the Banach Fixed-Point Theorem allows to prove the exponential convergence of the FPA. Even when the FPA does not converge, several iterated applications of the FPA may produce the desired fidelity. The FPA produces only small corrections in the control pulses and preserves the original bandwidth of the seed. The computational effort of each step of the FPA corresponds to the one of the numerical integration of a stabilized closed loop system. A piecewise-constant and a smooth numerical implementations are developed. Several numerical experiments with a N -qubit system illustrates the effectiveness of the method in several different applications including the conversion of piecewise-constant control pulses into smooth ones and the reduction of their bandwidth.