Preparation of Metrological State in Dipolar Interacting Spin Systems

The creation and control of highly entangled states lies at the heart of quantum metrology and promises sensing beyond the Standard Quantum Limit. Dipolar interacting spins in atomic and solid-state systems have recently emerged as an attractive candidate for engineering such states. This work discusses a novel variational method that efficiently generates metrologically relevant entangled states in small dipolar interacting spin ensembles using only limited qubit control and no knowledge of the actual spin configuration. Our results show that the generated entangled states provide sensitivity approaching the Heisenberg Limit. Depending on the depth of the variational ansatz the resulting metrological states resemble Greenberger–Horne–Zeilinger (GHZ) or Squeezed Spin states. We further show that these results hold in the presence of experimental imperfections, such as finite initialization/readout fidelity and coherence. The developed black-box variational optimization techniques provide a deeper understanding of the connections between spin arrangement (random vs regular arrays), entanglement, and obtainable sensitivity. Our results are directly applicable to systems in which the number of spins is limited, such as diamond-based nanoscale sensing.