A quantum retrograde canon: Complete population inversion in n 2-state systems

Alon Padan, Haim Suchowski

Research output: Contribution to journalArticlepeer-review


We present a novel approach for analytically reducing a family of time-dependent multi-state quantum control problems to two-state systems. The presented method translates between SU (2) × SU (2) related n2-state systems and two-state systems, such that the former undergo complete population inversion (CPI) if and only if the latter reach specific states. For even n, the method translates any two-state CPI scheme to a family of CPI schemes in n2-state systems. In particular, facilitating CPI in a four-state system via real time-dependent nearest-neighbors couplings is reduced to facilitating CPI in a two-level system. Furthermore, we show that the method can be used for operator control, and provide conditions for producing several universal gates for quantum computation as an example. In addition, we indicate a basis for utilizing the method in optimal control problems.

Original languageEnglish
Article number043021
JournalNew Journal of Physics
Issue number4
StatePublished - Apr 2018


  • coherent control
  • complete population transfer
  • quantum computation
  • quantum control
  • quantum information
  • quantum state transfer


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