Robust excitation of a large spin ensemble is a long-standing problem in the field of quantum information science and engineering and presents a grand challenge in quantum control. A formal theoretical treatment of this task is to formulate it as an ensemble control problem defined on an infinite-dimensional space. In this paper, we present a distinct perspective to understand and control quantum ensemble systems. Instead of directly analyzing spin ensemble systems defined on a Hilbert space, we transform them to a space where the systems have reduced dimensions with distinctive network structures through the introduction of moment representations. In particular, we illustrate the idea of moment quantization for a spin ensemble and illuminate how this technique leads to a dynamically equivalent control system of moments. This equivalence enables the control of spin ensembles through the control of their moment systems, which in turn creates a new control analysis and design paradigm for quantum ensemble systems based on the use of truncated moment systems.

Original languageEnglish
Pages (from-to)305-313
Number of pages9
JournalAnnual Reviews in Control
StatePublished - Jan 2022


  • Ensemble control
  • Moment representations
  • Quantization
  • Quantum ensembles


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