  We study the feasibility of implementing a quantum NOT gate (approximate)
when the quantum state lies between two latitudes on the Bloch's sphere and
present an analytical formula for the optimized 1-to-$M$ quantum NOT gate. Our
result generalizes previous results concerning quantum NOT gate for a quantum
state distributed uniformly on the whole Bloch sphere as well as the phase
covariant quantum state. We have also shown that such 1-to-$M$ optimized NOT
gate can be implemented using a sequential generation scheme via matrix product
states (MPS).
