Stabilizer circuits are classically tractable quantum circuits used extensively by quantum computer architects and coding theorists to design and benchmark protocols at scale in the absence of fault-tolerant machines. Despite their potentially attractive properties and a rich body of applications, there has been no qudit stabilizer simulator for $d > 2$. We introduce Sdim, modeled after Aaronson’s CHP and named after Gidney’s Stim, as the first realization of such a simulator, and have provided detailed case studies showing its utility. This abstraction will be the indispensable tool for qudit error correction as earlier stabilizer simulators have been for qubits.