Problem-Specific Basis Quantum State Readout via Proper Orthogonal Decomposition

Quantum computing is a promising technology for accelerating partial differential equation solvers applied to large-scale real-world problems. However, reconstructing a classical representation of the solution from the quantum state remains a significant bottleneck. We propose a problem-specific method, called proper orthogonal decomposition-based readout (PODR), to improve readout efficiency by precomputing characteristic features of the solution. The present method consists of an offline stage and an online stage. In the offline stage, a set of basis functions representing the dominant features of the target problem is constructed from representative solution data using classical computations. In the online stage, the quantum state is projected onto this reduced basis, and only the minimal set of weight coefficients is extracted to reconstruct the solution. Since the offline stage is carried out only once, the proposed PODR method is especially advantageous for simulations with varying parameters, which are common in computational fluid dynamics (CFD). Futhermore, we apply the proposed method to benchmark problems in fluid dynamics and demonstrate that PODR significantly reduces both the number of measurements and the computational resources in the online stage compared with conventional readout methods.