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Pauli basis measurements significantly impact MBQC execution:
Z-basis measurement: Removes the measured vertex and its edges. If the outcome is |1⟩, Pauli-Z gates are applied to all neighboring qubits.
Y-basis measurement: Equivalent to performing local complementation on the vertex before removal. Outcomes |+y⟩ and |-y⟩ require applying Rz(¥ð/2) and Rx(¥ð/2) to neighbors, respectively.
X-basis measurement: Requires local complementation on a neighbor, followed by Y-basis measurement on the vertex, and re-complementation on the neighbor. Specific outcome-dependent operations involve Ry(¡¾¥ð/2) and Z-gate applications.
These operations demonstrate the precision and complexity of Pauli measurements in quantum computation. |