Generative Circuit Design for Quantum-Selected Configuration Interaction

Abstract: Quantum-selected configuration interaction (QSCI) has emerged as a feasible approach for approximating electronic ground states on noisy quantum devices toward large-system demonstrations. In QSCI, Slater determinants are sampled from a quantum-prepared state, and the Hamiltonian is then diagonalized in the sampled subspace. To create a high-quality subspace under hardware constraints, the design of the state-preparation circuit is crucial. Here, we present a Generative Quantum Eigensolver (GQE)-based framework that optimizes ansatz structures using a Transformer policy trained on the QSCI subspace energy. We validate the framework on N2 in active spaces of up to 32 qubits. We found that the optimized circuits reach chemical precision with substantially lower gate counts than time-evolved circuits. Quantitatively, this corresponds to an average reduction of 98% in the required two-qubit gate count relative to the single-step first-order Trotterized approximation and 83% relative to the qDRIFT approximation. Furthermore, the resulting wavefunctions are competitive with heat-bath configuration interaction (HCI) in terms of compactness. In stretched-bond, strongly correlated regimes, they achieve chemical precision with subspaces that are 50% smaller than those required by HCI.