Quantum gate generation for systems with drift in U(n) using Lyapunov-LaSalle techniques
| Autor: | Pierre Rouchon, Hector Bessa Silveira, Paulo Sergio Pereira da Silva |
|---|---|
| Přispěvatelé: | Department of Automation and Systems (DAS), Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC), Department of Telecommunications and Control Engineering, Universidade de São Paulo = University of São Paulo (USP), QUANTum Information Circuits (QUANTIC), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Universidade de São Paulo (USP), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Pierre et Marie Curie - Paris 6 (UPMC)-MINES ParisTech - École nationale supérieure des mines de Paris, MINES ParisTech - École nationale supérieure des mines de Paris, Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Pierre et Marie Curie - Paris 6 (UPMC) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Lyapunov function
Discrete mathematics 0209 industrial biotechnology Lie group 02 engineering and technology State (functional analysis) 01 natural sciences Unitary state Computer Science Applications [SPI.AUTO]Engineering Sciences [physics]/Automatic symbols.namesake 020901 industrial engineering & automation Quantum gate [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Control and Systems Engineering Unitary group 0103 physical sciences symbols Initial value problem 010306 general physics Quantum ComputingMilieux_MISCELLANEOUS Mathematics SISTEMA QUÂNTICO |
| Zdroj: | International Journal of Control International Journal of Control, 2016, ⟨10.1080/00207179.2016.1161830⟩ Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP International Journal of Control, Taylor & Francis, 2016, ⟨10.1080/00207179.2016.1161830⟩ |
| ISSN: | 0020-7179 1366-5820 |
| DOI: | 10.1080/00207179.2016.1161830⟩ |
| Popis: | This paper considers right-invariant and controllable quantum systems with m inputs u = (u1,… , um) and state X(t) evolving on the unitary Lie group U(n). The e-steering problem is introduced and solved for systems with drift: given any initial condition X0 at the initial time instant t0 ≥ 0, any goal state Xgoal∈ U(n) and e > 0, find a control law such that dist(X(t0+t‾),Xgoal)≤ϵ, where t‾>0 is big enough and dist(X1, X2) is a convenient right-invariant notion of distance between two elements X1, X2 ∈ U(n). The purpose is to approximately generate arbitrary quantum gates corresponding to Xgoal. This is achieved by solving a tracking problem for a special kind of reference trajectories W‾: [t0, ∞) → U(n), which are here called c-universal reference trajectories. It is shown that, for this special kind of trajectories, the tracking problem can be solved up to an error e for any reference trajectory X‾(t)=W‾(t)R which is a right-translation of W‾(t), at least when dist(X(t0),X‾(t0)) is finite. Furth... |
| Databáze: | OpenAIRE |
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