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The Hadamard gate is a fundamental single-qubit quantum operation that transforms a qubit's state from a definite |0⟩ or |1⟩ to an equal superposition of both states, creating probabilistic behavior.
The Bloch sphere is a geometrical representation of a qubit's state, visualizing its superposition as a point on the surface of a unit sphere where axes represent classical bit values (0 and 1).
The T gate, a single-qubit rotation in quantum computing, applies a phase shift of -iπ/4 to the first qubit and π/4 to the second when acting on an entangled pair, crucial for certain quantum algorithms like Shor's.
A phase gate in quantum computing manipulates the relative phase between computational basis states of a qubit, crucial for implementing complex algorithms and achieving interference effects necessary for computation.
