The HHL Algorithm

HHL solves sparse linear systems in a quantum state - the primitive Kronos watches for the giant linear systems that come out of discretized transport and equilibrium PDEs.

The concept

Using phase estimation on e^(iAt), HHL prepares |x> with A|x> proportional to |b>, in time scaling with log of the system size - but only for well-conditioned, sparse A with efficient loading of b. You get a state, not the full vector: reading every entry erases the advantage.

How Kronos uses it

Discretizing plasma transport, equilibrium, or neutron-transport operators yields large sparse linear systems. Where Kronos needs a summary of the solution - an expectation value or a scalar response - rather than the whole field, HHL-style solvers are a candidate speedup being tracked in KODEX.

Honest note

The conditions are strict and the hardware demanding; this is a ~mid-2030s research target, with classical sparse solvers doing today's work.