Algorithmic analysis demonstrates residual-controlled quantum computing for AC power flow, highlighting reduced circuit depth and stable convergence under heavy loads.
Key Points
To develop an efficient quantum computing approach for AC power-flow analysis that mitigates error amplification from ill-conditioned Jacobian matrices and minimizes excessive quantum circuit depth.
Reformulated Newton corrections as Tikhonov-regularized least-squares subproblems within an inexact Newton framework, scaling state variables and power mismatches.
Approximated a bounded regularization filter using Chebyshev polynomials, enabling quantum singular-value transformation (QSVT) to directly transform Jacobian singular values.
Dynamically adapted the QSVT polynomial degree and quantum-solution precision according to outer power-flow residuals to manage block-encoding, polynomial, and measurement errors.
Proved theoretical boundedness of the regularized corrections and established a sufficient descent condition for quantum-approximate updates.
Characterized the formal relationship governing solution error and cumulative quantum query complexity under dynamically tuned precision controls.