Quantum Counting

Quantum counting estimates how many solutions a search space holds - useful to Kronos for gauging how many configurations satisfy a design constraint before enumerating them.

The concept

By applying phase estimation to Grover's operator, the rotation angle reveals the number of marked items M without listing them - combining amplitude amplification and phase estimation.

How Kronos uses it

In design-space work, knowing roughly how many configurations meet a set of gates (equilibrium, TBR, heat-flux) guides the search strategy and sets the right Grover iteration count for follow-up scans.

Honest note

A near-term classical estimate suffices today; the quantum version targets ~mid-2030s hardware.