Implementing symmetric entangling gates using quantum optimal control on nuclear-spin qudits in ⁸⁷Sr atoms

Qudits can be robustly encoded in nuclear spins of alkaline earth atoms and manipulated with magneto-optical fields.  In [1], we showed that how arbitrary SU(d) single-qudit unitary maps can be implemented in such systems using quantum optimal control. We applied this in the case of the I=9/2 nuclear spin in ⁸⁷Sr, a d=10 dimensional qudit, through a combination of nuclear spin-resonance and a tensor AC-Stark shift.  Augmenting our toolkit with Rydberg dressing allows us to create any symmetric entangling two-qudit gate such as CPHASE. Our techniques can be used to implement a qudit entangler for qudits from d=2 to d=10 encoded in the nuclear spin using partial isometries. We also studied how decoherence due to leakage affects the creation of qudit entanglers and found that we obtain a fidelity of 0.9931, 0.9849, and 0.9674 for d=3, d=5, and d=7 respectively.  This provides a powerful platform to explore the various applications of quantum information processing of qudits including metrological enhancement with qudits, quantum simulation, universal quantum computation, and quantum error correction.

[1] S. Omanakuttan, A. Mitra, M. J. Martin, and I. H. Deutsch,”Quantum Optimal Control of Nuclear Spin Qudecimals in 87Sr,” arXiv:2106.13705 (2021).