Predicting the Slow Drift of Nuclear Magnetic Noise in Semiconductor Spin Qubits

The dynamics of a nuclear spin bath generates magnetic noise that is a key contributor to the decoherence of electron spin qubits in electrostatically-defined quantum dots. Here we combine the quantum cluster correlation expansion (CCE) technique, which has already proven useful for predicting short-time solid-state qubit coherence, with classical rate matrices for the long-time behavior, enabling our simulations to span an unprecedentedly wide range of temporal regimes for understanding spin-bath dynamics. Our methodology is validated against experimental data from various silicon spin-qubit systems, demonstrating a strong agreement between simulated and measured correlation functions and power spectral densities (PSD). We also find that the nuclear bath dynamics can strongly depend on their interactions with the probing electrons (backaction). Furthermore, we deploy this model to predict the quantitative benefits from compensating for the slow drift of Overhauser fields in qubit operations. Our findings indicate that compensating for an Overhauser rotation measured △t in the past results in an effective T₂*, which we denote T₂*(△t) for clarity, under certain scenarios of interest, can be one or two orders of magnitude larger than the ergodic T₂* if the Overhauser rotation is re-characterized every 100 milliseconds. This work not only enhances our understanding of qubit dynamics but also provides a pathway for improving the operational fidelity of silicon-based quantum computing platforms.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U. S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.