  This paper studies a fundamental problem in convex optimization, which is to
solve semidefinite programming (SDP) with high accuracy. This paper follows
from the existing robust SDP-based interior point method analysis due to
[Huang, Jiang, Song, Tao and Zhang, FOCS 2022]. While, the previous work only
provides an efficient implementation in the classical setting. This work
provides a novel quantum implementation.
  We give a quantum second-order algorithm with high-accuracy in both the
optimality and the feasibility of its output, and its running time depending on
$\log(1/\epsilon)$ on well-conditioned instances. Due to the limitation of
quantum itself or first-order method, all the existing quantum SDP solvers
either have polynomial error dependence or low-accuracy in the feasibility.
