## Abstract

The quantum speed limit sets the minimum time required to transfer a quantum system completely into a

given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we

quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The

problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal

control algorithms. This approach leads to a necessary criterion for control optimality applicable as a measure

of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides

a robust prediction of the quantum speed limit and allows to adapt the control optimization such that it yields a

predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian,

and a classification scheme for the control sequences is proposed based on their optimizability.

given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we

quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The

problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal

control algorithms. This approach leads to a necessary criterion for control optimality applicable as a measure

of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides

a robust prediction of the quantum speed limit and allows to adapt the control optimization such that it yields a

predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian,

and a classification scheme for the control sequences is proposed based on their optimizability.

Originalsprog | Engelsk |
---|---|

Artikelnummer | 062106 |

Tidsskrift | Physical Review A |

Vol/bind | 92 |

Nummer | 6 |

Antal sider | 7 |

ISSN | 2469-9926 |

DOI | |

Status | Udgivet - 4 dec. 2015 |

## Emneord

- quant-ph
- cond-mat.quant-gas