Quantinuum and HQS Simulate 21-Spin NMR Spectrum on 42 Qubits With 1,400+ Two-Qubit Gate Circuits

Quantum hardware developer Quantinuum, in partnership with German software vendor HQS Quantum Simulations, has demonstrated an end-to-end digital Nuclear Magnetic Resonance (NMR) spectroscopy simulation on the Quantinuum System Model H2-1 trapped-ion quantum computer. The benchmark modeled the liquid-state proton NMR spectrum of 1,2-di-tert-butyl-diphosphane, a classically challenging 22-spin heteronuclear molecule containing two ³¹P nuclei and twenty ¹H nuclei.

To map the molecular spin network onto trapped-ion hardware, the joint team applied a hardware-efficient projection of the two-phosphorus subsystem into its singlet-triplet (|S⟩, |T₀⟩) subspace. This reduced the system from 22 physical spins to a 21-spin effective Hamiltonian, reducing two-qubit gate requirements per Trotter step from 69 to 20 native ZZPhase gates.

Previous 22-qubit hardware experiments on superconducting and trapped-ion systems struggled to resolve the 3.9–4.3 ppm region of diphosphane, which contains a subtle double-peak structure requiring up to fourth-order coupled-spin correlation tracking. By maintaining high gate fidelity across all-to-all connected ionic channels and mitigating idle memory errors, the H2-1 hardware run successfully reproduced the double-peak structure with a spectral resolution of approximately 0.07 ppm.

While the authors note that classical solvers like Spinach remain more computationally efficient for routine high-field liquid-state spectroscopy today, the result validates the viability of deep digital Hamiltonian simulation workflows for zero- to ultralow-field (ZULF) NMR and solid-state materials characterization.

Review the full pre-print manuscript on arXiv here and examine vendor performance analysis in the Quantinuum Blog here.

October 9, 2026