Quantum RVE solver in the NISQ regime

Abstract

Concurrent multiscale simulations in solid mechanics require repeated solutions of microscopic boundary-value problems. Quantum algorithms based on the quantum Fourier transform (QFT) offer a potential way to reduce this scaling exponentially. Previous work formulated a quantum homogenization algorithm for a onedimensional Representative Volume Element (RVE) by adapting the Fast Fourier transform (FFT) homogenization approach to a quantum computing setting. This work extends that formulation by investigating its feasibility on current quantum hardware. Three circuit models were implemented and compared: a full circuit following the original construction, a simplified circuit adapted to the geometry of the considered RVE, and a sequential circuit where the result of one quantum run is recovered and used as input for the next iteration. The circuits were first validated on a noiseless quantum circuit simulator and later executed on IBM quantum hardware using different error-suppression configurations. The hardware results showed that the fully quantum implementations are strongly limited by noise accumulation. The full circuits produced mostly noisy outputs, while the simplified circuit showed significant improvement, with average errors in the interval 23.91 − 36.19%. The best hardware results were obtained with the sequential circuit, which reduced the circuit depth and gate count and reached an average relative error of 25.00% (11% when limited to two iterations). The fully quantum models retain the expected O(poly(logN)) scaling. The sequential model, however, requires intermediate field recovery between QPU runs, making its complexity comparable to the classical FFT-based approach.