Two-Qubit Gate between GKP States in a Planar Superconducting Device

Combating decoherence inherent to quantum processors using quantum error correction (QEC) requires significant hardware resources. Bosonic QEC addresses this challenge by encoding quantum information within the infinite Hilbert space of harmonic oscillators, enabling protection against physical errors with only a moderate increase in hardware overhead. Previous demonstrations have shown that Gottesmann-Kitaev-Preskill (GKP) states encoded in resonators, coupled with a control qubit, can achieve break-even performance using open-loop stabilization protocols. However, experimental results with superconducting circuits have been limited to the control of a single logical qubit, lacking entangling operations between resonator states required for universal logical computation.

Here, we propose using the Linear Inductive Coupler as a three-wave-mixing element with which to perform fast, microwave-activated entangling interactions between two GKP qubits. Building on previous work, we aim to encode each GKP qubit within an on-chip resonator, coupled to a noise-biased fluxonium control qubit chosen to suppress bit-flip errors that degrade logical lifetimes. In this talk, we present progress towards the first demonstration of logical two-qubit gates between GKP states stabilized within our extensible planar architecture.