  We present protocols for implementation of universal quantum gates on an
arbitrary superposition of quantum states in a scalable solid-state Ising spin
quantum computer. The spin chain is composed of identical spins 1/2 with the
Ising interaction between the neighboring spins. The selective excitations of
the spins are provided by the gradient of the external magnetic field. The
protocols are built of rectangular radio-frequency pulses. The phase and
probability errors caused by unwanted transitions are minimized and computed
numerically.
