Лабораторная работа: Матрицы Паули и квантовая телепортация на IBM Quantum

Description This laboratory work presents a practical and theoretical study of Pauli matrices (X, Y, Z) and their fundamental role in quantum teleportation implemented on IBM Quantum hardware. The work explores the mathematical structure of single-qubit operations in a two-dimensional Hilbert space and their geometric interpretation as rotations on the Bloch sphere. A Bell state is prepared using Hadamard and CNOT gates, forming the entangled resource required for teleportation. The protocol is analyzed in matrix form, demonstrating how measurement outcomes correspond to Pauli correction operators (I, X, Z, XZ). The study emphasizes that quantum teleportation represents controlled amplitude and phase correction based on classical measurement results rather than physical transfer of matter. Special attention is given to the applied implementation on IBM Quantum, where Pauli operators are realized through physical microwave pulses corresponding to exponentials of SU(2) generators. While the work operates at the level of quantum circuits, it highlights the underlying algebraic structure of the Lie algebra su(2), which governs qubit rotations and quantum state evolution. The report integrates mathematical formalism, circuit-level realization, and physical interpretation, providing a coherent understanding of the role of Pauli operators in quantum information processing.