Dressed Qubits in Nuclear Spin Baths

We present a method to encode a \textit{dressed} qubit into the product state of an electron spin localized in quantum dot and its surrounding nuclear spins via a dressing transformation. In this scheme, the hyperfine coupling and a portion of nuclear dipole dipole interaction become logic gates, while they are the sources of decoherence in electron spin qubit proposals. We discuss errors and corrections for the dressed qubits. Interestingly, the effective Hamiltonian of nuclear spins is equivalent to a pairing Hamiltonian, which provides the microscopic mechanism to protect dressed qubits against decoherence.