  This dissertation explores quantum computation using qudits encoded into
large spins, emphasizing the concept of quantum co-design to harness the unique
capabilities of physical platforms for enhanced quantum information processing.
First, we delve into the generation of high-fidelity universal gate sets for
quantum computation with qudits. Leveraging principles from quantum optimal
control, Rydberg physics, and the atomic structure of alkaline-earth atoms, we
propose protocols for high-fidelity universal gate sets in the ground state of
87Sr with reasonable experimental parameters. Next, we analyze schemes to
encode a qubit in the large spin qudits for fault-tolerant quantum computation
(FTQC). By comprehending the most dominant noise in the physical system, we
develop FTQC protocols that outperform the standard protocols. Finally,
considering spin qudits for neutral atom quantum computation, we studied
protocols for converting leakage errors to erasure errors resource efficiently.
Also, we developed cooling methods for neutral atoms without destroying the
quantum information.
