We study the ability to control $d$ -dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semianalytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semianalytic protocol is compared to a brute-force, full numerical search. For small inhomogeneities, $<$ $1%$ , both approaches achieve average fidelities greater than 0.99, but the brute-force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble.We study the ability to control $d$-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semianalytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semianalytic protocol is compared to a brute-force, full numerical search. For small inhomogeneities, $<$$1%$, both approaches achieve average fidelities greater than 0.99, but the brute-force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble.

arXiv:1109.0146Physical Review AFeb 3, 201237 citations

Controlling Three Atomic Qubits

Hartmut Häffner, Mark Riebe, Ferdinand Schmidt‐Kaler +9 more

Mar 1, 20060 citations

Single-qudit control in Sr 87 via optical nuclear electric resonance

Johannes K. Krondorfer, Matthias Diez, Andreas W. Hauser

Optical nuclear electric resonance (ONER) was recently proposed as a fast and robust single-qubit gate mechanism in Sr 87 . Here, we demonstrate through numerical simulations that ONER can be extended to single-qudit control, addressing multiple one-level hyperfine transitions within the ten-dimensional nuclear-spin manifold. We identify suitable operating regimes and show that ONER enables high-fidelity spin manipulations, with simulated π-gate fidelities exceeding 99.9%, while maintaining coherence under realistic parameter fluctuations. These results establish a proof of principle for optical qudit control in Sr 87 and delineate practical parameter ranges for future experiments, highlighting ONER as a promising pathway toward high-dimensional quantum information processing.Optical nuclear electric resonance (ONER) was recently proposed as a fast and robust single-qubit gate mechanism in Sr 87 . Here, we demonstrate through numerical simulations that ONER can be extended to single-qudit control, addressing multiple one-level hyperfine transitions within the ten-dimensional nuclear-spin manifold. We identify suitable operating regimes and show that ONER enables high-fidelity spin manipulations, with simulated π-gate fidelities exceeding 99.9%, while maintaining coherence under realistic parameter fluctuations. These results establish a proof of principle for optical qudit control in Sr 87 and delineate practical parameter ranges for future experiments, highlighting ONER as a promising pathway toward high-dimensional quantum information processing.

arXiv:2506.23143Physical Review ANov 20, 20251 citation

Building Robust Qubits

Dave Bacon

Bulletin of the American Physical SocietyMay 19, 20060 citations

Realizing quantum gates with optically addressable Yb + 171 ion qudits

Mikhail A. Aksenov, Ilia V. Zalivako, Ilya A. Semerikov +6 more

The use of multilevel information carriers, also known as qudits, is a promising path for exploring scalability of quantum computing devices. Here we present a proof-of-principle realization of a quantum processor register that uses optically addressed $^{171}\mathrm{Yb}^{+}$ ion qudits in a linear trap. The rich level structure of $^{171}\mathrm{Yb}^{+}$ ions allows using the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and a two-qudit M\o{}lmer-S\o{}rensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way toward further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of $^{171}\mathrm{Yb}^{+}$ ion qudits.The use of multilevel information carriers, also known as qudits, is a promising path for exploring scalability of quantum computing devices. Here we present a proof-of-principle realization of a quantum processor register that uses optically addressed $^{171}\mathrm{Yb}^{+}$ ion qudits in a linear trap. The rich level structure of $^{171}\mathrm{Yb}^{+}$ ions allows using the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and a two-qudit M\o{}lmer-S\o{}rensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way toward further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of $^{171}\mathrm{Yb}^{+}$ ion qudits.

arXiv:2210.09121Physical Review AMay 23, 202345 citations

We study the ability to control

d

-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semianalytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semianalytic protocol is compared to a brute-force, full numerical search. For small inhomogeneities,

<

1%

, both approaches achieve average fidelities greater than 0.99, but the brute-force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble.

^{171}\mathrm{Yb}^{+}

ion qudits in a linear trap. The rich level structure of

^{171}\mathrm{Yb}^{+}

ions allows using the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and a two-qudit M\o{}lmer-S\o{}rensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way toward further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of

^{171}\mathrm{Yb}^{+}

ion qudits.