Transformer-Accelerated Variational Quantum Eigensolvers via Parameter Warm-Starting

Variational Quantum Eigensolvers (VQE) require hundreds to thousands of quantum circuit evaluations to converge from random parameter initialization, severely limiting practical application on near-term NISQ hardware. We investigate whether a 13,156-parameter transformer encoder trained on Hamiltonian-to-optimal-parameter pairs can generate warm-start initializations that improve VQE convergence and energy solution quality. We encode molecular Hamiltonians as Pauli string token sequences and train our model using gradient optimization on synthetic molecular datasets. Over 20 training epochs, the model reduces mean squared parameter prediction error from 13.786 to 4.555 (a 67% reduction). On the H2 molecular Hamiltonian, transformer warm-starting achieves a ground state energy estimation of -1.5181 Hartree, outperforming the random-initialization baseline (-1.4950 Hartree). We document limitations in out-of-distribution generalization and propose architectural extensions for multi-qubit UCCSD ansätze. All source code and test suite: https://github.com/aashiq-parinda/quantum-genai-warmstart