Acc-VQLS: Accelerated Variational Quantum Linear Solver for VSC Simulation

Voltage source converters (VSCs) play a critical role in modern power systems, where their simulation requires solving linear system problems and remains computationally expensive. Quantum linear system solvers, particularly the variational quantum linear solver (VQLS) tailored for noisy intermediate-scale quantum devices, offer a competitive paradigm with the potential for developing linear solvers with logarithmically scaled computational complexity. We propose Acc-VQLS, a domain-specific quantum algorithm and circuit co-optimization method that accelerates traditional VQLS for VSC simulation. We adopt constant vector-based variational quantum circuits for fast convergence with efficient initial state preparation and employ multi-core processing to parallelize the cost function evaluation and gradient computation. To demonstrate the potential applicability of Acc-VQLS in VSC operating scenarios, we employ the commonly used fault behavior model for VQLS-based VSC simulation. Quantitative experimental evaluations and comparisons across the tested benchmarks show that the proposed Acc-VQLS reduces iterations required for cost function convergence by an average of 82.5%, and our multi-core parallel computing strategy achieves a 53.9 × speedup on the AMD EPYC 9554 CPU. By incorporating a short-circuit fault in the VSC simulation, the proposed Acc-VQLS with error compensation achieves less than 10 ^{− 9} in both the mean absolute error and the root mean square error.