The Quantum Geometry® Grand Challenge: A Multiyear Prize and Benchmark Program for Quantum Computing in Geometry, CAD, GIS, and Meshing

Abstract

This paper proposes the Quantum Geometry® Grand Challenge, a five-year prize and benchmark program for quantum and hybrid quantum–classical methods in computational geometry, computer-aided design (CAD), geographic information science (GIS), and meshing. The central question is where, if anywhere, quantum computation improves a complete geometric workflow. Comparisons would include data preparation, encoding, execution, and output validation. The program would begin by defining benchmarks, without requiring an initial demonstration of quantum advantage. A proposed 2027 pilot would select a small number of spatial-optimization and mesh-partitioning problems and publish classical reference solvers and independent validators. Separate award categories would recognize reproducible positive and negative findings. Two illustrative problems show how the evaluation would work. The paper sets out submission requirements, comparison metrics, judging safeguards, and a staged expansion to CAD, geometric algorithms, and data representations. Quantum Geometry® LLC would initially administer the program and offer conditional founding matching support of up to $100,000 over five years. Expansion would depend on secured resources and independently reproducible pilot results. The contribution is a research-program design that can be tested and evaluation resources that others can reuse; it is not a claim of demonstrated quantum advantage.