Sparse Quantum Voxel Encoding for Readout-Efficient Molecular Geometry Reconstruction on NISQ Devices
This work addresses the challenge of efficiently reconstructing molecular geometries on noisy intermediate-scale quantum (NISQ) devices, where conventional full-state tomography incurs prohibitive exponential measurement overhead. The authors propose a sparse voxel encoding scheme that discretizes molecular space into a three-dimensional voxel grid, mapping atomic positions and species to a single computational basis state and thereby constructing a sparse equal-amplitude superposition. This formulation recasts geometry reconstruction as a support recovery problem under computational-basis sampling. The approach reduces measurement complexity from exponential to $O(A \log A)$, where $A$ is the number of atoms. Demonstrated on IBM’s 156-qubit Kingston device, the method reconstructs the discretized geometry of a 10-atom ethylamine molecule with high recall using only approximately $10^2$ measurements, significantly enhancing readout efficiency on NISQ hardware.