Jonas Mielke

Nuclear spins are promising for quantum information applications due to their long coherence times. However, the underlying good isolation from the environment is a challenge for readout and the implementation of mutual interactions between them.
Previously, experiments have realized a hybrid system in which an electron is shared between a quantum dot and $^{31}$P donor atom implementing a electron spin-nuclear spin flip-flop qubit. Employing ac-magnetic fields, this system can be harnessed to couple the nuclear spin to microwave cavity photons [1,2]. A related system with an electron confined in a double quantum dot and subject to a magnetic field gradient constitutes a flopping mode electron spin qubit that couples to cavity photons by electrical means [3,4].

We envision an architecture combining the key ideas of the two aforementioned systems and theoretically investigate the interaction between a nuclear spin with a microwave cavity by electrical means and thereby demonstrate nuclear spin readout by probing the cavity transmission [5]. Furthermore, we find that driving the QD-donor system allows to compensate the frequency mismatch between the donor nuclear spin and the resonator mode and also enables an effective nuclear spin-photon coupling. While this coupling cannot be tuned to the strong coupling regime, we predict that coupling the nuclear spins of two distant QD-donor systems dispersively to the microwave resonator allows the implementation of a resonator-mediated nuclear-spin two-qubit $\sqrt{\mbox{iSWAP}}$ gate with a gate fidelity exceeding 90%.

[1] Tosi et al., PRB 98, 075131 (2018)
[2] Tosi et al., Nature Comm. 8, 450 (2017)
[3] Benito et al., PRB 96, 235434 (2017)
[4] Mi et al., Nature 555, 7698 (2018)
[5] J. Mielke, J. R. Petta, and G. Burkard, PRX Quantum 2, 020347 (2021)