Pulse control of superconducting cavity-based qudits with a Fock-state basis

Fock-basis-encoding qudits allow quantum gates to operate on multiple qudit levels simultaneously. This capability is advantageous for applications involving complex local gate operations, such as the digital quantum simulation of non-Abelian gauge theories. However, compiling unitary operations to native qudit gates remains a challenging task, often requiring substantial computational resources. In this work, we theoretically investigate the direct pulse control of a superconducting radio-frequency cavity coupled to an ancilla transmon for gate synthesis. We will discuss the improvements and limitations applicable to high Fock states. This work paves the way toward more efficient and robust qudit-gate synthesis.