SUMMARY Quantum computers hold the promise of being able to solve some challenging problems sometime in the next decade or two. Here we explore how to exploit their potential power in an unusual tomographic challenge: Can one estimate material percentages such as net-to-gross or sand-shale ratios using sparse offset-traveltime information? By restricting the constituent materials in an isotropic horizontally-stratified medium to a specific set with wellknown acoustic (or elastic) properties, transmission tomography can, in principle, provide the relative fraction of each material within the set of layers over which the ray traverses. In this paper, we formulate an algorithm for this "super-resolution" calculation suitable for quantum computing. INTRODUCTION In a horizontally-stratified isotropic medium, one may arbitrarily permute the layers between source and receivers without changing the recorded traveltime of the direct arrival.