A fixed point algorithm for improving fidelity of quantum gates
| Autor: | Pierre Rouchon, Hector Bessa Silveira, Paulo Sergio Pereira da Silva |
|---|---|
| Přispěvatelé: | Polytechnic School of the University of São Paulo (Brazil), Universidade de São Paulo (USP), Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), QUANTum Information Circuits (QUANTIC), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC), Universidade de São Paulo = University of São Paulo (USP), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Controllability
0209 industrial biotechnology Control and Optimization Context (language use) 02 engineering and technology Topology 01 natural sciences Mathematics Subject Classification. 93D05 93D30 8108 [SPI.AUTO]Engineering Sciences [physics]/Automatic Reduction (complexity) 020901 industrial engineering & automation Quantum gate [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] 0103 physical sciences Right-invariant systems 010306 general physics Mathematics Banach Fixed-Point Theorem Banach fixed-point theorem Bandwidth (signal processing) Computer Science::Software Engineering Quantum control Numerical integration Computational Mathematics Control and Systems Engineering Iterated function Qubit Lyapunov stability |
| Zdroj: | ESAIM: Control, Optimisation and Calculus of Variations ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2021, 27, pp.S9. ⟨10.1051/cocv/2020057⟩ ESAIM: Control, Optimisation and Calculus of Variations, 2021, 27, pp.S9. ⟨10.1051/cocv/2020057⟩ |
| ISSN: | 1292-8119 1262-3377 |
| DOI: | 10.1051/cocv/2020057⟩ |
| Popis: | This 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. |
| Databáze: | OpenAIRE |
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