Self-correcting GKP qubit and gates in a driven-dissipative circuit

Understand

We show that a self-correcting GKP qubit can be realized with a high-impedance LC circuit coupled to a resistor and a Josephson junction via a controllable switch.

• When activating the switch in a particular stepwise pattern, the resonator relaxes into a subspace of GKP states that encode a protected qubit.
• Under continued operation, the resistor dissipatively error-corrects the qubit against bit flips and decoherence by absorbing noise-induced entropy.
• We show that this leads to an exponential enhancement of coherence time (T1 and T2), even in the presence of extrinsic noise, imperfect control, and device parameter variations.