Heisenberg propagation of a Pauli observable through a Clifford circuit
= Heisenberg propagation of a Pauli observable through a Clifford circuit
To compute a single-qubit output probability of a <Clifford gate>[Clifford circuit], propagate its measured Pauli observable backward through the circuit. Every conjugation remains a tensor-product Pauli, whose expectation on a <product state> factors into efficiently computable one-qubit expectations.