Quantum Newtonian Power Flow

This letter introduces a novel quantum Newtonian power flow (QNPF) algorithm. The QNPF features a more general quantum circuit that can process non-Hermitian matrices with fewer required qubits and eliminates the need for iterative optimization of gate parameters. Our contributions include: 1) Developing a quantum state-based Newton's power flow framework to enhance accuracy, convergence, and versatility; 2) Integrating quantum singular value transformation to efficiently solve each iteration of QNPF with scalable quantum circuits; and 3) Devising a block-rescaling technique to ensure computational accuracy in ill-conditioned cases. Test results validate the accuracy, scalability and numerical stability of QNPF, underscoring its potential to advance quantum power flow computation.