Logarithmic QMA repetition rounds reach exponential target error
ProvedShiQMAConstructiveSchedule.error_roundsamplificationpolynomial-boundsqmaquantum-complexity
The scalar majority error after the constructive round count is at most 2 raised to minus the target polynomial value.
Preamble
import Definitions.Def_ShiQMAConstructiveSchedule import Theorems.Thm_ShiQMAErrorIteration_dyadic_error_bound import Theorems.Thm_ShiQMAConstructiveSchedule_eval_le_pow_budget set_option autoImplicit false set_option maxHeartbeats 2000000 open ShiQMAConstructiveSchedule ShiQMAErrorIteration
Formal statement
theorem ShiQMAConstructiveSchedule.error_rounds (p : Polynomial ℕ) (n : ℕ) :
error (rounds p n) ≤ ((1 : ℝ) / 2) ^ (p.eval n) := by sorrySource