Towards Quantum Computing Enhanced General Computational Homogenization Without Readout Problem

This work introduces a quantum computing method for general computational homogenization problems. Beyond homogenization of composite materials, these problems appear in broader computational mechanics areas characterized by a common mathematical structure: solving a linear system and then evaluating a scalar effective property. While quantum linear solvers offer potential speedups for solving the linear system, their utility has been limited by the quantum readout problem, which is the prohibitive cost of reconstructing the full solution vector from its quantum state. We address this problem by developing an efficient readout method that computes the target scalar directly from the quantum state, bypassing the need for full state reconstruction. The method is demonstrated through the computational homogenization of composite materials, where the homogenized stress is calculated by only two probability estimations from the quantum state. To verify the proposed method, we first obtain a solution vector using a quantum linear solver on a simulator, and then conduct experiments of the readout method on a real superconducting quantum processor, yielding results with moderate accuracy despite current noisy quantum hardware limitations. This work presents a potential solution to the readout problem in quantum computing applications for computational mechanics.