Cutting Quantum Circuits Beyond Qubits

We extend quantum circuit cutting to heterogeneous registers comprising mixed-dimensional qudits. By decomposing non-local interactions into tensor products of local generalised Gell-Mann matrices, we enable the simulation and execution of high-dimensional circuits on disconnected hardware fragments. We validate this framework on qubit--qutrit ($2$--$3$) interfaces, achieving exact state reconstruction with a Total Variation Distance of 0 within single-precision floating-point tolerance. Furthermore, we demonstrate the memory advantage in an 8-particle, dimension-8 system, reducing memory usage from 128 MB to 64 KB per circuit.