The extremely reduced dimension of spin qubits implemented in electrostatically defined quantum dots has made them one of the forerunners in the quest of implementing a quantum processor. However, the implementation of more performing gate operations has required the integration of micromagnetic structures, increasing the footprint of a single spin-qubit substantially .
A parallel approach to implementing high-fidelity universal control, while retaining a small qubit footprint, can be reached by harnessing the slowly fluctuating Overhauser gradient in gallium arsenide. It has been shown that magnetic field gradients as strong as 70 MHz can be reached, for a duration much longer than the life and coherence time of the qubit . Taking advantage of on-board FPGA capabilities integrated with qubit readout and control packaged in a single Operator-X (OPX) machine , we report on Hamiltonian estimation in a gallium arsenide double-quantum dot. The arbitrary Overhauser gradient between the two quantum dots encoding a singlet-triplet qubit is estimated on-the-fly by the OPX server, enabling feedback protocols within a few µs. Concurrently, a QDAC  is synced to the OPX module and is used to continuously maintain the optimal DC biasing for the quantum hardware and acquire sub-second charge stability maps. The real-time estimation makes it possible to obtain coherent universal control of the qubit, without requiring micromagnets or nuclear polarization protocols.
 Philips, Stephan G. J., Mądzik, Mateusz T., Amitonov, Sergey V., et al. Universal control of a six-qubit quantum processor in silicon. arXiv:2202.09252 (2022).
 Shulman, M., Harvey, S., Nichol, J. et al. Suppressing qubit dephasing using real-time Hamiltonian estimation. Nat Commun 5, 5156 (2014).
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