### 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 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 (US) |
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Article number | 125304 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 53 |

Issue number | 12 |

DOIs | |

State | Published - Mar 3 2020 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Keywords

- Quantum control
- Quantum information
- Speed limits

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## Cite this

Lee, J., Arenz, C., Burgarth, D., & Rabitz, H. (2020). An upper bound on the time required to implement unitary operations.

*Journal of Physics A: Mathematical and Theoretical*,*53*(12), [125304]. https://doi.org/10.1088/1751-8121/ab7498