The roles of drift and control field constraints upon quantum control speed limits

Christian Arenz, Benjamin Russell, Daniel Burgarth, Herschel Rabitz

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In this work we derive a lower bound for the minimum time required to implement a target unitary transformation through a classical time-dependent field in a closed quantum system. The bound depends on the target gate, the strength of the internal Hamiltonian and the highest permitted control field amplitude. These findings reveal some properties of the reachable set of operations, explicitly analyzed for a single qubit. Moreover, for fully controllable systems, we identify a lower bound for the time at which all unitary gates become reachable. We use numerical gate optimization in order to study the tightness of the obtained bounds. It is shown that in the single qubit case our analytical findings describe the relationship between the highest control field amplitude and the minimum evolution time remarkably well. Finally, we discuss both challenges and ways forward for obtaining tighter bounds for higher dimensional systems, offering a discussion about the mathematical form and the physical meaning of the bound
Original languageEnglish
Article number103015
JournalNew Journal of Physics
Issue number10
Early online date26 Jul 2017
Publication statusPublished - 20 Oct 2017


  • speed limits
  • quantum control
  • unitary gates
  • quantum information


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