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