Unary quantum clock
= Unary quantum clock
{title2=$|c_t\rangle=|1\rangle^{\otimes t}|0\rangle^{\otimes(T-t)}$}
A <unary quantum clock> represents step $t$ of a $T$-gate circuit by $|1\rangle^{\otimes t}|0\rangle^{\otimes(T-t)}$. Clock strings are orthogonal, and adjacent legal strings differ at one qubit. Local patterns around that change permit a <history-subspace propagation Hamiltonian> with bounded locality.