Scalable Quantum Molecular Generation via GPU-Accelerated Tensor-Network Simulation

Abstract

We propose Scalable Quantum Molecular Generation (SQMG), a variational quantum-circuit for sampling molecular graphs using chemical priors on atoms and bonds. SQMG assigns a fixed 3-qubit register to each heavy atom and reuses a single 2-qubit bond register to generate bonds sequentially, yielding an ''atom no-reuse, bond reuse'' architecture with linear qubit scaling. Measurement results are mapped to molecular graphs via lightweight classical decoding with structural constraints. In CUDA-Q, we benchmark the state-vector simulation (CPU/GPU) and the tensor-network simulation (GPU). At $N=8$ heavy atoms, the state-vector simulator (GPU) and the tensor-network simulator (GPU) achieve speeds of up to $4.5\times 10^{4}$ and $2.2\times 10^{3}$ over the state-vector (CPU) baseline, respectively. Crucially, tensor-network simulation extends exact simulation to $N=40$ heavy atoms, where state-vector methods become memory-limited. For training, Bayesian optimization outperforms COBYLA on a Validity$\times$Uniqueness objective, and the same architecture supports \textit{de novo} generation, scaffold decoration, and linker design. Overall, SQMG provides a scalable, reproducible testbed for evaluating accelerated tensor-network simulation and future quantum molecular generation algorithms.