Planted Pauli Hamiltonians Expose a Direct Route to Benchmarking Quantum Scalability Before Full Error Correction Arrives

This arXiv preprint (v1, June 2026) proposes a theoretical construction of Pauli Hamiltonians whose ground-state energies are known exactly by embedding a planted block-product state within frustration-free local clauses. The method exposes the model solely as a polynomial-size sum of Pauli operators, optionally conjugated by Clifford circuits, and subsumes classical planted CSPs as the diagonal case. No hardware experiments or sample sizes are reported; the work remains a purely constructive framework with open-source instances provided for verification. Unlike prior benchmarking sets that rely on numerical certification or small-system diagonalization, this approach inherits classical hardness directly while remaining efficiently preparable on quantum hardware. Original coverage overlooks how the construction sidesteps the need for full fault tolerance during early scalability tests, offering a verifiable primitive that can probe the precise crossover where logical error rates drop below physical rates—an acute bottleneck unaddressed by random-Hamiltonian or supremacy-style benchmarks. Related analyses in the VQE literature (see Tilly et al., Phys. Rev. X 12, 011003) show that ground-state estimation accuracy collapses once qubit counts exceed roughly 50 without error mitigation; the planted instances here supply known targets that can quantify that collapse systematically. A second connection appears in surface-code threshold studies (Fowler et al., Phys. Rev. A 86, 032324), where the same Clifford-preserving spectrum property aligns with stabilizer measurements, allowing the benchmark to double as a diagnostic for logical-qubit overhead before full code distances are reached. Limitations include the absence of noise-model integration and the assumption that the planted state remains dominant under realistic decoherence—both untested.