During each outer iteration we compute the residual in the preconditioned space, i.e.,
Because (K \ll N) (typically (K\le30) for matrices up to (10^7) rows), the quantum portion contributes a overhead, while the dominant linear term is handled classically but with a dramatically reduced effective condition number thanks to the quantum subspace. juq470
Quantum algorithms, notably the Harrow‑Hassidim‑Lloyd (HHL) algorithm [1], theoretically solve such systems in with respect to (N). However, practical deployment of HHL is hampered by: During each outer iteration we compute the residual
It’s possible that:
The authors typically suggest several mitigation strategies: the quantum portion contributes a overhead