Some local Hamiltonians have a "history" state as its ground state. It is a superposition over snapshots of a quantum computation. The terms in this superposition need to be locally connected (or checkable). First, we will review how this can be done with clock constructions – domain-wall (unary), pulse (tuned to a single excitation), and geometric (data moving on a lattice). Second, we will discuss the various ways of preferring proper clock states – in frustration-free ways, or using frustrated gadgets. Finally, we will look at composite clocks (q-3-SAT) as well as new ideas beyond unary clocks, asking whether they could possibly lead to better eigenvalue/promise gaps.

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