Overlapotron: Zero-Shot Molecular Transfer for Quantum State Preparation

Fault-tolerant quantum algorithms for chemistry need an initial state with high overlap with the target state, and the Hartree–Fock overlap decays exponentially with molecular size. Current methods build that state for one molecule at a time, from a classical solution of that same molecule or from a per-molecule quantum optimization. We propose Overlapotron, a model that predicts the initial-state preparation circuit of an unseen molecule from the molecule alone, with no target state and no per-molecule optimization at test time. An equivariant molecular-orbital encoder feeds heads whose output size follows the molecule while the learned weights stay fixed. We show transfer in two regimes. On exact state-vector targets, the heads emit unitary coupled cluster with singles and doubles (UCCSD) and coupled exchange operator (CEO) circuits. On density matrix renormalization group (DMRG) matrix product state (MPS) targets computed at a fixed bond dimension, we introduce the brickwall family, whose overlap with an MPS contracts as a tensor network, so training scales past the state-vector limit. One brickwall model trained on 25,877 QM7 states of at most 88 qubits transfers to QM9 targets of 90 to 112 qubits. Its predicted circuits exceed the overlap of a target-aware non-variational benchmark that compiles each target state directly, at $43\%$ of its T count and $11\%$ of its T depth. On held-out hydrogen chains of 68 to 100 qubits, the margin over the benchmark averages $5\times$ and grows to $8\times$ on the longest chain. Two new datasets of 30,000 CASCI state vectors and 7,165 DMRG matrix product states, with a 25,877-state geometry sweep, support the training.