 Computational history state

A computational history state coherently records a circuit's intermediate states with orthogonal clock labels: $(T+1{)}^{-1/2}{\sum }_{t=0}^T|{\psi }_t⟩|c_t⟩$. A propagation term penalizes a mismatch between adjacent time labels and the corresponding gate. With correct propagation, uniform coefficients form a zero-energy ground state within the history subspace.