Universal Hamiltonian control in a planar trimon circuit

Multimode circuits provide an avenue for flexible control of single and multi-qubit gates. In this work we implement a multimode circuit known as a trimon integrated in a planar geometry. The trimon features three transmon-like modes with strong all-to-all $ZZ$ coupling. We demonstrate high fidelity operations on the trimon, achieving flexible control of its rich state space. This includes qubit rotations conditioned on one or both other qubits, unconditional single-qubit rotations, and both excitation-conserving and double-excitation two-qubit entangling gates. Through multi-tone driving we are able to implement all 16 two-qubit Pauli operators in the two-qubit space. We further demonstrate using the trimon as a qudit with up to 8 states and higher coherence than typical transmon-based implementations. Our results show a compact, highly controllable device that can potentially replace transmons in standard superconducting processor architectures.