Entropy quantum computing for fixed-backbone protein design

Computational protein design (CPD) is a central problem in biotechnology, with applications in enzyme engineering and therapeutic design, but its combinatorial complexity poses a significant challenge for classical optimization methods. In this work, we formulate fixed-backbone CPD as a quadratic Hamiltonian over rotamer variables, enabling solution using Quantum Computing Inc.'s photonic entropy computing platform, Dirac-3. We evaluate solution quality by benchmarking against an exact classical cost function network (CFN) solver, which provides provably optimal baselines. On a set of standard benchmark proteins ranging from 493 to 943 variables, Dirac-3 produces best-observed solutions (over 100 samples per instance) within 0.16-2.47% of the optimal energies. These results show that the proposed formulation can identify low-energy configurations on directly solvable CPD instances, while sample-level energy distributions vary by instance. Runtime behavior is reported over the tested regime, where CFN remains faster in absolute terms, while Dirac-3 exhibits moderate growth in runtime with problem size. This study focuses on optimization performance as measured by energy relative to exact baselines under a pairwise fixed-backbone energy model. Exploratory experiments on larger instances using decomposition-based approaches are provided in the Supplementary Material. Overall, the results establish a benchmark for entropy-based optimization on CPD formulations within the directly solvable regime.