 History-subspace propagation Hamiltonian

In the orthonormal history basis $|e_t⟩=|{\psi }_t⟩|c_t⟩$, circuit propagation restricts to $E=\frac{1}{2}{\sum }_{t=1}^T(|e_t⟩-|e_{t-1}⟩)(⟨e_t|-⟨e_{t-1}|)$. This is a graph Laplacian on a path. Its uniform zero-energy vector is the computational history state, while initialization restricts to $D=I-|e_0⟩⟨e_0|$.