Universal SU(8) control of a high-spin nucleus in silicon*

We have developed a global rotation control scheme for controlling the nucleus of the high-spin 123Sb donor (I=7/2) implanted in silicon – an appealing platform for realization of quantum processors [1] and for exploration of quantum chaos [2]. As opposed to individually addressing the transition between pairs of energy levels (‘ladder climbing’), in this scheme a multi-frequency control pulse drives all the NMR frequencies simultaneously, allowing one to implement global rotations defined in I=7/2 Bloch sphere, i.e. SU(8) rotation operators. In practice, an FPGA-based AWG generates multichromatic RF pulses and handles a ‘generalized rotating frame’ [3] by keeping track of multiple phases at each of the nuclear resonance frequencies. Multiple future experimental endeavours can benefit from implementing global rotations. For example, it allows to more efficiently initialize arbitrary quantum states compared to the conventional 'ladder-climbing' protocol. Special states of interests are spin coherent states in arbitrary directions, Schrödinger’s cat states, and logical qubits encoding in high-spin nuclei [4].

 

[1] S. Asaad et al., Nature 579, 205–209 (2020)

[2] V. Mourik et al., Phys. Rev. E 98, 042206 (2018)

[3] M. Leuenberger and D. Loss, Phys. Rev. B 68, 165317 (2003)

[4] J. A. Gross, Phys. Rev. Lett. 127(1), 010504 (2021)