Generative Krylov Quantum Diagonalization

Variational quantum algorithms face ansatz bias and noisy, costly energy reads on today's devices. Recent generative approaches instead learn to propose circuits directly, suggesting a path to reduce per-problem optimization. We present an AI-for-quantum workflow that avoids per-problem energy minimization in favor of learned state synthesis for Krylov subspace methods. In this talk, we will focus on a conditional generative model that constructs a shallow, problem-aware initial circuit followed by the construction of a Krylov subspace on quantum computer. The resulting projected Hamiltonian is then classically diagonalized on an HPC system to yield low-lying spectra. We introduce context-aware transfer across problems via an encoder architecture guided by domain knowledge while limiting circuit depth. Our method provides a novel co-design of generative AI and quantum Krylov methods that enables per-problem tuning with reusable priors and highlights the growing role of AI for early-fault-tolerant quantum computing applications.