Towards Dissipative Stabilization of Four-Legged Cat Qubits in Superconducting Circuits : Part I

Dynamical stabilization of bosonic qubits offers a hardware-efficient route to quantum error correction by exploiting the high dimensionality of bosonic modes to redundantly encode quantum information. In particular, dissipative Schrödinger cat qubits exhibit an exponential suppression of bit-flip errors with increasing cat size, at the cost of a linear growth in phase-flip errors. Dissipative stabilization of two-component cat states can be realized by injecting and dissipating pairs of excitations in a target resonator.

This principle can, in turn, be extended to stabilize the four-component Schrödinger cat code, which maintains similar bit-flip protection while providing first-order suppression of phase-flip errors. Here, quartets of excitations must be injected and dissipated in the target mode, requiring high-order multi-photonic processes. These processes naturally arise in high-impedance Josephson circuits, but are accompanied by additional multi-photonic interactions that must be carefully controlled.

This two-part talk will introduce the dynamical stabilization scheme and a superconducting circuit designed to implement it, followed by recent experimental progress toward four-legged cat stabilization.

Part I will discuss the stabilization mechanism, unintended multi-photonic interactions, and resulting design constraints.