Quantum HHL algorithm applied to electric circuit and line transmission wave

The HHL quantum algorithm [1] is a procedure that addresses the resolution of linear systems of equations (QLSP). Under certain conditions, the algorithm has a logarithmic order in the number of equations, better than the faster classical method. The algorithm manages to find a quantum state proportional to the solution vector, up to a normalization factor. The disadvantage is that to determine each of the coefficients of the solution vector, the algorithm’s output quantum state must be determined with additional statistical methods, thus losing its exponential advantage. There are certain types of problems in which this disadvantage can be circumvented, the statistical treatment is unavoidable, but for certain cases such as electrical circuits, in which the main interest is to find only one of the currents, (for example the load current), we only need to measure one of the qubits of the solution state. In this article we solve the linear system associated with the currents of an electrical circuit with sinusoidal voltage, using the HHL algorithm, simulated in a Scilab numerical environment. An optimized example of an electrical line transmission wave in a real computer on the IBMQ platform, is also solved