Quantum Gate Operations 3 | Special Superposition States #quantumcomputing

The +, -, i, and -i states are special quantum states that lie on the equator of the Bloch sphere, representing equal superpositions of the computational basis states (|0⟩ and |1⟩) but with different phase relationships. The + state is an equal combination of |0⟩ and |1⟩ with no relative phase, while the - state has the same combination but with a phase shift that results in destructive interference when measured in the + basis. The i state introduces an imaginary phase, shifting the superposition in a way that aligns it along a different equatorial axis, and the -i state represents the same superposition but in the opposite phase direction. These states are critical in quantum computing, as they define key quantum gates and enable complex interference effects in quantum algorithms.