Tick-tock Goes the Clock
summary
Claims an improvement of the promise gap in history‑state Hamiltonian constructions from about 1/L^3 to 1/L^2 by analyzing clock spectra; shows the clock always induces a quantum‑walk gap scaling like 1/L^2 on a line, and gives concrete clock encodings (pulse clock, domain wall clock), gadget recipes (third‑order ancilla generation, perturbative gadgets) to reduce locality to 3‑ and 2‑local at the cost of shrinking gaps with system size; reports dimensional tradeoffs (8–13‑dim particles, 2D grids) and where the construction succeeds or incurs overhead.
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chapters (6)
- 0:00Start
- 1:29The OMA protocol
- 13:23Snapshots of a computation
- 15:03The data & the clock locally comparing related states
- 17:17Making a local clock
- 34:53Lower locality (3-LH) for the price of bad transitions
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