Quantum computing in decoherence-free subspaces with coupled charge qubits

We present a simple but feasible quantum computing scheme in decoherence-free subspace by coupling four identical superconducting Josephson circuits. Two physical charge qubits are encoded to a logical one by connecting them with a common superconducting quantum interference device (SQUID). Well-controllable coupling between two logic qubits is further proposed by using a variable electrostatic transformer to construct the two-qubits controlled-phase gate. Taking into account the symmetry of system-bath interaction, our scheme may be helpful to suppress collective noises.