Sparse Quantum Voxel Encoding for Readout-Efficient Molecular Geometry Reconstruction on NISQ Devices

Quantum machine learning models for molecular design often struggle with a measurement bottleneck: encoding molecular structures into quantum states is easy, but extracting that information back into a usable 3D geometry typically requires full quantum state tomography. This process is exponentially expensive, making it impractical for near-term Noisy Intermediate-Scale Quantum (NISQ) devices. The authors address this by proposing a new encoding scheme that makes molecular readout efficient and scalable.

The researchers propose a "voxelization encoding" strategy. They discretize the 3D space surrounding a molecule into a grid of voxels. Each atom's position and chemical species are mapped to a unique integer index, which is then encoded into a computational basis state. The entire molecule is represented as an equal superposition of these basis states.

Because the information is stored in the support of the quantum state (i.e., which basis states are occupied) rather than in the complex amplitudes, the reconstruction problem is transformed into a "coupon collector" problem. Instead of performing full tomography, one can simply sample the quantum state in the computational basis repeatedly to identify all occupied voxels. This reduces the measurement cost from exponential to polynomial, specifically requiring O(A log A) shots for an A-atom molecule.

The authors validated their approach on the 156-qubit IBM Kingston device using an 8-qubit circuit to represent a 10-atom ethylamine molecule. Despite significant hardware noise, they achieved high reconstruction recall (up to 98% with 200 shots). This demonstrates a two-to-three order of magnitude reduction in measurement requirements compared to traditional amplitude encoding methods that require full tomography. The study confirms that this voxelization approach is a practical, readout-efficient representation for molecular geometry on current quantum hardware.