Twirling and Hamiltonian engineering via dynamical decoupling for Gottesman-Kitaev-Preskill quantum computing

I introduce an energy constrained approximate twirling operation that can be used to diagonalize effective logical channels in Gottesman-Kitaev-Preskill (GKP) quantum error correction, project states into the GKP code space and construct a dynamical decoupling sequence with fast displacements pulses to distill the GKP stabilizer Hamiltonians from a suitable substrate Hamiltonian. The latter is given by an LC oscillator comprising a superinductance in parallel to a Josephson Junction. This platform, in principle, allows for protected GKP quantum computing without explicit stabilizer measurements or state reset by dynamically generating a "passively" stabilized GKP qubit.