Robust control and entanglement of qudits in neutral atom arrays

Quantum devices comprised of elementary components with more than two stable levels—so-called qudits—enrich the accessible Hilbert space, enabling applications ranging from fault-tolerant quantum computing to simulating complex many-body models. While several quantum platforms are built from local elements that are equipped with a rich spectrum of stable energy levels, schemes for the efficient control and entanglement of qudits are scarce. Importantly, no experimental demonstration of multiqudit control has been achieved to date in neutral atom arrays. Here, we propose a general scheme for controlling and entangling qudits and perform a full analysis for the case of qutrits, encoded in ground and metastable states of alkaline earth atoms. We find an efficient implementation of single-qudit gates via the simultaneous driving of multiple transition frequencies. For entangling operations, we provide a concrete and intuitive recipe for the controlled- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi mathvariant="script">Z</a:mi> </a:math> ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi mathvariant="normal">C</c:mi> <c:mi mathvariant="script">Z</c:mi> </c:mrow> </c:math> ) gate for any local dimension <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>d</f:mi> </f:math> , realized through alternating single qudit and entangling pulses that simultaneously drive up to two Rydberg transitions. We further prove that two simultaneous Rydberg tones are, in general, the minimum necessary for implementing the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi mathvariant="normal">C</g:mi> <g:mi mathvariant="script">Z</g:mi> </g:mrow> </g:math> gate with a global drive. The pulses we use are optimally controlled, smooth, and robust to realistic experimental imperfections, as we demonstrate using extensive noise simulations. This amounts to a minimal, resource-efficient, and practical protocol for realizing a universal set of gates. Our scheme for the native control of qudits in a neutral atom array provides a high-fidelity route toward qudit-based quantum computation, ready for implementation on near-term devices.