Qronecker: A Certifiable Kronecker Compression Primitive for Quantum-Chemistry Hamiltonians

Processing qubit Hamiltonians derived from electronic-structure problems can become classically prohibitive because many downstream manipulations still rely on dense operator constructions whose cost grows exponentially with qubit number. We introduce Qronecker, a cut-aware low-rank Kronecker decomposition algorithm that turns Hamiltonian compression into a certifiable, resource-aware decision primitive. Operating entirely in Pauli coefficient space, Qronecker avoids forming dense 2^n x 2^n matrices, constructs low-rank Kronecker approximations under a chosen bipartition, and returns both an instance-specific compressibility curve and a state-independent worst-case energy certificate that links rank and cut choices to conservative energy-deviation bounds. Across molecular benchmarks comprising hundreds of systems up to 30 qubits, we find that traceless low-rank structure is common but heterogeneous: many screened systems reach high coefficient-space fidelity at low rank, yielding large savings in classical preprocessing and conditional reductions in downstream circuit-resource proxies, while the certificate remains valid but conservative on the auditable subset. The same analysis shows that fixed global fidelity targets are not generally sufficient for chemistry-level guarantees, motivating adaptive rank and cut selection. These results position Qronecker as a certifiable compression primitive for rank and cut selection in quantum-chemistry Hamiltonian processing.