# Overhauser Field estimation

In this video we introduce contemporary fine-tuning task: Overhauser field estimation that stems from interaction of nuclear and electron spin and influences qubit frequency. We show how to formulate Overhauser field gradient estimation as a Hamiltonian learning task and discuss possible generalizations.

# Main takeaways

- Nuclear spin of the quantum dot material can influence the qubit frequency
- Overhauser field gradient is time dependent, and, for appropriate qubit operation, it needs to be tracked contemporaneously during the experiment
- Overhauser field can be predicted with a neural network mapping measurements on a Hamiltonian parameter

# Further thinking

True or False: Overhauser field gradient is a function of time and keeps changing on the scale of typical quantum dot experiment.

# Further reading

Suppressing qubit dephasing using real-time Hamiltonian estimation: https://www.nature.com/articles/ncomms6156

Hamiltonian estimation using the Bayesian inference method of the Overhauser field.

Spectrum of the Nuclear Environment for GaAs Spin Qubits: https://arxiv.org/abs/1701.01855

This experiment recovers the Overhauser field from the qubit precession. Main figures in the notebooks are taken from this paper.

Supplementary information for ”Spectrum of the Nuclear Environment for GaAs Spin Qubits”: https://journals.aps.org/prl/supplemental/10.1103/PhysRevLett.118.177702/Overhauser_supplement.pdf

Measurement of Temporal Correlations of the Overhauser Field in a Double Quantum Dot: https://arxiv.org/abs/0712.4033

A classical model of Overhauser field fluctuations due to nuclear spin diffusion is used to fit the experimental data in Fig. 2(c) in the notebook.

Characterizing non-Markovian Quantum Processes by Fast Bayesian Tomography: https://arxiv.org/abs/2307.12452

Experimental implementation of future prediction for Overhauser Field Gradient.