Universal Uhrig Dynamical Decoupling for Bosonic Systems

We construct efficient deterministic dynamical decoupling schemes protecting continuous-variable degrees of freedom. Our schemes target decoherence induced by quadratic system-bath interactions with analytic time dependence. We show how to suppress such interactions to Nth order using only N pulses. Furthermore, we show how to homogenize a 2(m)-mode bosonic system using only (N + 1)(2m+1) pulses, yielding-up to the Nth order-an effective evolution described by noninteracting harmonic oscillators with identical frequencies. The decoupled and homogenized system provides natural decoherence-free subspaces for encoding quantum information. Our schemes only require pulses which are tensor products of single-mode passive Gaussian unitaries and SWAP gates between pairs of modes.