Figure 3: Schematics of the N-qubit model described in Example A.

Straight edges represent the Heisenberg interactions, while the triple edge represents the three-body interaction among qubits 1–3. The red part in the upper figure corresponds to H⁽¹⁾ acting on qubits 1 and 2, while the remainder including a local term Z₃ on qubit 3 corresponds to H⁽²⁾ acting on all the N qubits. The Zeno projection P₁ on qubit 1 transforms the upper Hamiltonians to the lower model, where the state of qubit 1 is frozen, while we are left with a Heisenberg chain with the local term Z₃ and a control on qubit 2. The Lie algebra of the upper system is only two dimensional, while the lower allows us to perform full control over the system apart from the frozen qubit 1.