Planar multi-mode superconducting circuit design for high-dimensional computation

Transmon qubits have recently been advanced as the building blocks of noisy intermediate-scale quantum processors. In these quantum processors and building blocks, multi-qubit gate fidelity and interqubit connectivity becomes crucial, wherein transmons create a bottleneck due to weak transverse coupling among nearest-neighbor qubits. Multi-mode superconducting qubits, or multimons, are demonstrated as an alternative, where fully-connected qubits with strong longitudinal coupling form hybridized modes to achieve high-fidelity multi-qubit gates over a larger Hilbert space. With this approach, a three-qubit system is demonstrated with a complete gate set using 3D superconducting cavities, the latter of which can be less susceptible for large-scale integration [1,2,3]. For this purpose, we propose planar coupling strategies for multimons inspired by state-of-the-art planar topologies of Josephson ring modulator-based devices [4, 5]. In this work, we successfully coupled two pairs of coplanar waveguide resonators to a trimon with equal strength in a differential configuration to effectively control and readout a three-qubit system through the two hybridized longitudinal modes. We also proposed a coupling scheme between multiple trimons for scalable quantum processors.