Nonadaptive Clifford measurement pattern

A path graph state simulates a sequence of Clifford gates $J({\alpha }_j)$, ${\alpha }_j\in \{0,\pi /2\}$, using fixed equatorial qubit measurement bases on successive path vertices. Let $s_j$ be raw outcomes, $t_j=2{\alpha }_j/\pi \in \{0,1\}$, and start the Pauli frame at $a_0=b_0=0$. Matrix commutation and $J(-\pi /2)=XJ(\pi /2)$ giveInduction shows the final unmeasured state differs from the ideal circuit output by $X^{a_m}{Z}^{b_m}$, up to global phase. A final computational basis result $d$ is corrected to $d\oplus a_m$. All bases are fixed, and projectors on distinct vertices commute, so all measurements, including the final one, can occur in a single layer. The frame recurrence is classical outcome processing, not quantum feed-forward.

Compile each CNOT gate into a Hadamard gate, a Controlled-Z gate, and another Hadamard gate on its target. Every one-bit teleportation implementing a Hadamard gate uses a fixed angle-zero basis. A Pauli frame propagates by classical binary updates without changing a measurement basis. All internal measurements, and any fixed computational output measurements, therefore share one simultaneous layer. Resource preparation and classical processing are not included in this logical measurement depth.