Note B.4.1. Physical Interpretation of Quantum Gates.
A quantum gate is not merely a matehmatical operation. It is the unitary time-evolution operator generated by a specific, engineered Hamiltonian acting on a physical system for a controlled duration.
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Single Qubit Gates: Correspond to rotations of the the Bloch vector induced by external fields (e.g., magnetic, electric, optical, etc.).
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Two Qubit Gates: Correspond to turning on an interaction Hamiltionian (coupling) between subsystems, generating entanglement.