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Prepare an ancilla qubit in $|0⟩$. To measure $X\otimes X$, apply a Hadamard gate to each data qubit, apply a controlled-NOT gate from each data qubit to the ancilla, measure the ancilla in the computational basis, and apply a Hadamard gate to each data qubit again. The ancilla records the parity of the two rotated computational-basis bits, so outcome $0$ corresponds to eigenvalue $+1$ and outcome $1$ to eigenvalue $-1$. The data register is projected by $[I+(-1{)}^{s}X\otimes X]/2$, so its complete post-measurement state is retained. For $Z\otimes X$, perform the same ancilla-assisted Pauli measurement but apply the basis-changing Hadamard gates only to the second data qubit.

A Pauli-based computation starts with the supplied nonstabilizer resource state $|\alpha ⟩$ and performs an adaptive sequence of mutually commuting measurements of Pauli observables. Each outcome is recorded classically and may determine the next Pauli observable and the final classical output. When a proposed observable anticommutes with a previously fixed Pauli constraint, its outcome is uniformly random by part b(i); one samples that outcome and uses the Clifford operation $V({\lambda }_P,{\lambda }_Q)$ from part b(ii) to update the Clifford frame. This replaces the old constraint by the newly measured one while preserving the distribution and the post-measurement state represented by the computation.