Preparation of decoherence-free cluster states with optical superlattices

We present a protocol to prepare decoherence-free cluster states using ultracold atoms loaded in a two dimensional superlattice. The superlattice geometry leads to an array of 2×2 plaquettes, each of them holding four spin- 1,2 particles that can be used for encoding a single logical qubit in the twofold singlet subspace, insensitive to uniform magnetic field fluctuations in any direction. Dynamical manipulation of the supperlattice yields distinct inter- and intraplaquette interactions and permits us to realize one qubit and two qubit gates with high fidelity, leading to the generation of universal cluster states for measurement based quantum computation. Our proposal based on inter- and intraplaquette interactions also opens the path to study polymerized Hamiltonians which support ground states describing arbitrary quantum circuits. © 2009 The American Physical Society.