A Quantum Computing Method for AC Power Flow with Residual-Controlled Dynamic Precision.

To address the amplification of correction errors caused by an ill-conditioned AC power-flow Jacobian under heavily loaded operating conditions, as well as the excessive circuit depth associated with a fixed quantum-solution accuracy, this paper proposes a residual-controlled, regularized quantum singular-value transformation (QSVT) method within an inexact Newton power-flow framework. First, the power-mismatch vector and state variables are scaled, and the Newton correction is reformulated as a Tikhonov-regularized least-squares subproblem. A bounded regularization filter is then approximated using Chebyshev polynomials, allowing QSVT to directly transform the singular values of the Jacobian matrix. On this basis, the residual of the linear subproblem associated with the quantum-approximate correction is defined, and constraints are established to relate the polynomial-approximation error, block-encoding error, and quantum measurement error to the inexact Newton forcing term. The QSVT polynomial degree and quantum-solution accuracy are subsequently adjusted dynamically according to the outer power-flow residual. Theoretical analysis establishes the boundedness of the regularized correction, a sufficient descent condition for the quantum-approximate correction, and the relationship between the solution error and cumulative query complexity under dynamically controlled quantum accuracy.