  We introduce a scheme for realizing arbitrary controlled-unitary operations
in a two qubit system. If the 2 \times 2 unitary matrix is special unitary (has
unit determinant), the controlled-unitary gate operation can be realized in a
single pulse operation. The pulse, in our scheme, will constitute varying one
of the parameters of the system between an arbitrarily maximum and a
"calculated" minimum value. This parameter will constitute the variable
parameter of the system while the other parameters, which include the coupling
between the two qubits, will be treated as fixed parameters. The values of the
parameters are what we solve for using our approach in order to realize an
arbitrary controlled-unitary operation. We further show that the computational
complexity of the operation is no greater than that required for a
Controlled-NOT (CNOT) gate. Since conventional schemes realize a
controlled-unitary operation by breaking it into a sequence of single-qubit and
CNOT gate operations, our method is an improvement because we not only require
lesser time duration, but also fewer control lines, to implement the same
operation. To demonstrate improvement over other schemes, we show, as examples,
how two controlled-unitary operations, one being the controlled-Hadamard gate,
can be realized in a single pulse operation using our scheme. Furthermore, our
method can be applied to a wide range of coupling schemes and can be used to
realize gate operations between two qubits coupled via Ising, Heisenberg and
anisotropic interactions.
