Variational Quantum Algorithm as an Efficient Tool for Data Fitting

This study explores the suitability of the variational quantum data fitting method as an enabling tool to better understand and characterize power system analytics. A recently proposed algorithm, the Variational Quantum Linear Solver (VQLS) is investigated as an efficient approach to analyze power systems. In most studies so far, the VQLS technique has been primarily applied to square matrices. However, many problems in the analysis of power systems are represented by tall matrices. In this paper, we study the transformation of tall matrices into a form suitable for the VQLS algorithm. Two computing methodologies are explored: Internal Multiplication and Hermitian Expansion. Preliminary results show that for a sample matrix of size 64×16, Hermitian expansion requires a minimum of 7 qubits and a significantly longer computational time to prepare unitaries, as compared to Internal Multiplication which requires just 4 qubits and a significantly shorter computational time to prepare unitaries. Preliminary results also show that under the condition that matrix A has orthonormal column vectors, the Euclidean distance between vectors of answers from quantum and classical methods exhibits a slight discrepancy beyond 6 qubits. Furthermore, the technique has a polynomial scaling (in terms of qubits), which is an improvement compared to classical algorithms of UP to eight qubits.