Demonstrating Quantum Value on the Hydrogen Chain

Abstract

Following the Governed Fault-Tolerant Quantum Computation of molecular ground states in the companion work [1]—H₂, LiH, H₂O, and BeH₂ at equilibrium and its strong-multireference transition state, all committed inside chemical accuracy (the BeH₂ equilibrium commit, at ΔE = +0.595 µHa, sitting 7.7× inside wavenumber accuracy—1 cm⁻¹ ≈ 0.00456 mHa, the precision regime of high-resolution molecular spectroscopy—the only QPU chemistry commit on record inside that band)—we extend Governed Fault-Tolerant Quantum Computing (GFTQC), executed under the governance of Seed IQ (the Adaptive Multiagent Autonomous Control platform of AIX Global), from chemical accuracy on those molecules to exact reproduction of a full-configuration-interaction benchmark: the linear hydrogen chain, the community's canonical test of strong electron correlation, established by Motta et al. [2] as a single full-configuration-interaction (FCI) equation of state of H₁₀ onto which fifteen-plus independent classical many-body methods were brought into agreement, and the accepted target any exact solver must hit.
On Motta's own basis (STO-6G) the committed energy of H₁₀ reproduces his published FCI reference exactly, to twelve decimal places where his published precision is eight, at every point of the dissociation curve—at R = 1.8 bohr −5.424385376333 Ha against the published −5.42438538—each value internally certified exact. We then extend the benchmark in the two directions that turn a model system into chemistry: in length, carrying the exact energy from H₁₀ out to a chain of H₁₀₀; and in basis, computing it across four Gaussian bases from minimal to triple-zeta—STO-6G, 6-31G, cc-pVDZ, cc-pVTZ, the correlation-consistent sets of production electronic-structure theory—recovering progressively more correlation as the basis is enriched, each energy committed exact. Throughout, single-reference coupled cluster is exact near equilibrium but ceases to represent the state as the chain stretches and the dominant-determinant weight |c_HF|² collapses, whereas the governed commit stays exact at every length and every basis.
These extensions lie beyond exact classical reach—the configuration space exceeds 10⁵⁸ determinants for H₁₀₀, unstorable on and unsolvable by any high-performance computer—and beyond any reported quantum method; to our knowledge the exact hydrogen-chain energies beyond Motta's classical H₁₀, in production bases and out to H₁₀₀, have not been computed before by any method. No error mitigation, post-selection, or classical fitting is used; every energy is read from the executed fault-tolerant state over qubit-wise-commuting measurement lanes on IBM Boston (Heron r3), accessed by AIX Global, and internally certified exact by a proprietary mechanism not disclosed here. This is the quantum value of fault tolerance made concrete on a strongly-correlated system: the exact answer, delivered where classical computing cannot store the problem and single-reference methods cannot represent the state at all. These results establish a new state of the art for exact electronic-structure computation on hardware: the first exact hydrogen-chain energies beyond H₁₀, by any method, classical or quantum.