QVAE-Mole: The Quantum VAE with Spherical Latent Variable Learning for 3-D Molecule Generation

Molecule generation ideally in its 3-D form has enjoyed wide applications in material, chemistry, life science, etc. We propose the first quantum parametric circuit for 3-D molecule generation for its potential quantum advantage especially considering the arrival of Noisy Intermediate-Scale Quantum (NISQ) era. We choose the Variational AutoEncoder (VAE) scheme for its simplicity and one-shot generation ability, which we believe is more quantum-friendly compared with the auto-regressive generative models or diffusion models as used in classic approaches. Specifically, we present a quantum encoding scheme designed for 3-D molecules with qubits complexity $\mathcal{O}(C\log n)$ ($n$ is the number of atoms) and adopt a von Mises-Fisher (vMF) distributed latent space to meet the inherent coherence of the quantum system. We further design to encode conditions into quantum circuits for property-specified generation. Experimentally, our model could generate plausible 3-D molecules and achieve competitive quantitative performance with significantly reduced circuit parameters compared with their classic counterparts. The source code will be released upon publication.