Native multi-qubit gates on a single-junction unimon circuit

Quantum processors with native multi-qubit gates may offer very efficient implementations of near-term quantum algorithms on noisy hardware. Here, we introduce the multiunimon, a superconducting multimode circuit that encodes multiple qubits and enables native multi-qubit gates in a device consisting of a single Josephson junction embedded in a coplanar waveguide structure. Closely related to the unimon qubit, it inherits properties such as high anharmonicity, full protection against low-frequency charge noise, and partial protection against flux noise. By designing such a three-qubit device with Josephson-to-inductive energy ratio above unity and using a leakage-aware encoding scheme for the computational states, we simulate all twelve different controlled-controlled-NOT gates with a mean fidelity of 99.5% with simple sine-squared pulses of comparable length to single-qubit gates. The performance is limited by incoherent errors dominated by dielectric loss. With improvements in noise protection, design, and pulse shaping, the simulations suggest that fidelities approaching 99.99% are within reach. Our results demonstrate the potential of the multiunimon as a highly connected multi-qubit unit for larger superconducting quantum processors.