Hardware efficient autonomous error correction protocol (Part II)

A crucial component of our scheme to implement the Very small Logical Qubit (VSLQ) Hamiltonian is an inter-qutrit coupling mechanism capable of generating strong interactions between various two-qutrit levels while maintaining a small cross-Kerr interaction. We discuss our design of a tunable inductive coupler that can produce relevant blue and red sidebands with rates greater than 6 MHz and suppresses ZZ coupling at the operating DC flux point. We also achieve qutrit-resonator blue sideband rates above 1 MHz which is more than sufficient for the VSLQ protocol. We demonstrate our preliminary results of the logical state stabilization and corresponding improvements in the logical relaxation times. Finally, we discuss the challenges behind realizing the full autonomous quantum error correction where six microwave drives are needed to stabilize an unknown logical superposition state.