## Abstract

We derive an upper bound for the time needed to implement a generic unitary transformation in a d dimensional quantum system using d control fields. We show that given the ability to control the diagonal elements of the Hamiltonian, which allows for implementing any unitary transformation under the premise of controllability, the time *T* needed is upper bounded by where *g*_{min} is the smallest coupling constant present in the system. We study the tightness of the bound by numerically investigating randomly generated systems, with specific focus on a system consisting of *d* energy levels that interact in a tight-binding like manner.

Original language | English |
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Article number | 125304 |

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 53 |

Issue number | 12 |

DOIs | |

Publication status | Published - 27 Mar 2020 |

## Keywords

- Quantum control
- Quantum information
- Speed limits