Qubits Are Not Enough: Deflation and Measurement Limits in Variational Quantum Modal Analysis

Amplitude encoding stores an N-degree-of-freedom structural mode using ceiling(log2 N) qubits. This article develops an evaluation framework for variational quantum eigensolvers in finite-element structural dynamics. A Cholesky transformation maps the generalized eigenproblem to a symmetric mass-orthonormal Hamiltonian, ensuring Euclidean quantum-state orthogonality equals structural mass orthogonality. For higher modes, the deflation penalty condition is sharpened to a necessary-and-sufficient threshold, with a Davis-Kahan bound quantifying effects of approximate projectors. Numerical studies separate mapping correctness, ansatz expressibility, preprocessing, Pauli growth, finite-shot uncertainty, and damage localization. For 128-DOF chains, consistent-mass whitening increases transformed-operator density from 0.023 to 0.308 and Pauli terms from 576 to 2950. Exact state-vector experiments show qubit count and circuit expressibility are distinct. At 10^5 shots per Pauli term, first-mode frequency RMS error is 2.45%. In an oracle-state study, 10% stiffness loss is localized in 84.5% of trials. Results sharpen the deflation condition, quantify resource bottlenecks, and claim no speedup.

Source: arXiv:2610.31393v1 - http://arxiv.org/abs/2610.31393v1 PDF: https://arxiv.org/pdf/2610.31393v1 Original Link: http://arxiv.org/abs/2610.31393v1