Quantum optimal control of ten-level nuclear spin qudits in Sr 87

Journal Article · 16 December 2021 · Physical Review A

DOI: https://doi.org/10.1103/physreva.104.l060401 · OSTI ID:1863739

Omanakuttan, Sivaprasad  ^[1]; Mitra, Anupam ^[1]; Martin, Michael J.  ^[2]; Deutsch, Ivan H.  ^[1]

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1. Univ. of New Mexico, Albuquerque, NM (United States). Center for Quantum Information and Control
2. Univ. of New Mexico, Albuquerque, NM (United States). Center for Quantum Information and Control; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We study the ability to implement unitary maps on states of the $I=9/2$ nuclear spin in ${}_{87}\mathrm{Sr}$, a $d=10$ dimensional (qudecimal) Hilbert space, using quantum optimal control. Through a combination of nuclear spin resonance and a tensor ac Stark shift, by solely modulating the phase of a radio-frequency magnetic field, the system is quantum controllable. Alkaline-earth-metal atoms, such as ${}_{87}\mathrm{Sr}$, have a very favorable figure of merit for such control due to narrow intercombination lines and the large hyperfine splitting in the excited states. We numerically study the quantum speed limit, optimal parameters, and the fidelity of arbitrary state preparation and full SU(10) maps, including the presence of decoherence due to optical pumping induced by the light-shifting laser. We also study the use of robust control to mitigate some dephasing due to inhomogeneities in the light shift. We find that with an rf Rabi frequency of ${\mathrm{\Omega }}_{\text{rf}}$ and 0.5% inhomogeneity in the the light shift we can prepare an arbitrary Haar-random state in a time $T=4.5\pi /{\mathrm{\Omega }}_{\text{rf}}$ with average fidelity $\left({\mathcal{F}}_{\psi }\right)=0.9992$, and an arbitrary Haar-random SU(10) map in a time $T=24\pi /{\mathrm{\Omega }}_{\text{rf}}$ with average fidelity $\left({\mathcal{F}}_U\right)=0.9923$.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1863739
• Report Number(s): LA-UR-21-25988
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 6 Vol. 104; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English