Newton-Raphson Method Using HHL Algorithm for Power Flow Quantum Computing
Ziad El-Khatib, Sherif Moussa · 2024
This paper presents Newton-Raphson method using HHL algorithm for power flow quantum computation. The proposed Newton-Raphson HHL Quantum method converges to the solution within four iterations compared to the Newton-Raphson classical solution which converged in five iterations. The Newton-Raphson classical solution voltage$\mathrm{V}_{2}=0.96674$pu, angle$\delta_{2}=-0.04816$rads, angle$\delta_{3}=0.04096$rads. The Newton-Raphson-HHL Quantum method voltage$\mathrm{V}_{2}= 0.98173$pu, angle$\delta_{2}=-0.05018$rads, angle$\delta_{3}=0.04021$rads. This work Newton-Raphson HHL Quantum method for 3-bus time to converge is O.$228\mathrm{s}$. The fidelity is calculated to be 0.981436 with circuit width of 4 which is the number of qubits used in the circuit and the circuit depth gate layers is 126.