  We describe how to implement quantum logic operations in a silicon-based
quantum computer with phosphorus atoms serving as qubits. The information is
stored in the states of nuclear spins and the conditional logic operations are
implemented through the electron spins using nuclear-electron hyperfine and
electron-electron exchange interactions. The electrons in our computer should
stay coherent only during implementation of one Control-Not gate. The exchange
interaction is constant and selective excitations are provided by a magnetic
field gradient. The quantum logic operations are implemented by rectangular
radio-frequency pulses. This architecture is scalable and does not require
manufacturing nanoscale electronic gates. As shown in this paper parameters of
a quantum protocol can be derived analytically even for a computer with a large
number of qubits using our perturbation approach. We present the protocol for
initialization of the nuclear spins and the protocol for creation of
entanglement. All analytical results are tested numerically using a two-qubit
system.
