Limited connectivity makes nonlocal quantum gates expensive on near-neighbor hardware, where compilation typically relies on swap transport, inheriting both depth overhead and path congestion. We present a swap-free routing framework in which higher levels of a qudit act as orthogonal spectral buses that transport control information without moving the computational state. We show that exact congestion relief in nearest-neighbor architectures requires local Hilbert-space expansion. In this model, a single nonlocal operation over a path of length $L$ requires a best-case minimum of $2L+1$ logical routing primitives. For comparison, a layout-restoring swap implementation requires $2L$ swap operations ($6L$ cnot-equivalent layers). Overlapping routes remain distinguishable through bus labels encoded in the same physical qudits. This routing algebra extends to Boolean fan-in at a common target: Multiple controls arriving on distinct buses trigger a local unitary based on an arbitrary Boolean function of bus digits, yielding multicontrol operations of depth $2L+D_g+O\left(K\right)$ for fan-in size $K$ to account for shared-target serialization, where $D_g$ is the target-synthesis cost. We prove decodability, reversibility, and correctness for cnot and Boolean fan-in, along with a state-count lower bound $d\ge 2^{K+1}$ for exact overlap routing. Cirq simulations confirm single-control correctness and zero crosstalk. Compiler-level benchmarks on quantum Fourier transform, quantum approximate optimization algorithm, and mirror-interaction circuits verify the predicted congestion law and transport reduction. Noisy QuTiP simulations show that the architectural advantage depends on higher-level coherence and speed. These results identify spectral qudit routing as a congestion-relief architecture that separates nonlocal control delivery from local target-side aggregation, providing a minimal mechanism for overcoming qubit routing limitations.

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• Quantum circuits
• Quantum engineering