Precise entanglement generation in spin registers coupled to defects

Understanding multipartite entanglement is one of the key ingredients for the development of precise control protocols for multi-qubit quantum architectures. In solid-state defect platforms, the generation of electron-nuclear entanglement is challenging due to the always-on interactions. In this talk, I will present a general description of the electron-nuclear spin entanglement from the perspective of the entangling gate design. This description is a new analytical framework which characterizes the entanglement within an arbitrarily large electron-nuclear spin register, quantifies cross-talk, and identifies optimal decoupling sequences for nuclear spin control. I will show how this formalism can be exploited to speed-up the entanglement generation through single-shot multipartite gates, and additionally how to saturate all-way correlations in the presence of error-rates applicable to state-of-the-art defect systems.