A verified quantum advantage for a chemically relevant ground-state energy
Difficulty 65.5: requires error-corrected hardware beyond present scale and a classical frontier that keeps moving (DMRG and coupled-cluster results on FeMoco and Fe4S4 models); somewhat harder than the verifiable-quantum-advantage benchmark (50). Application value 61.5: it would validate the main commercial case for chemistry on quantum computers. Leverage 56: it shapes funding, algorithms and classical benchmarks.
The problem
No quantum computer has yet beaten the best ordinary methods at calculating the energy of a real molecule.
- 1Hope: quantum beats classical for molecules
- 2Present machines small and noisy
- 3Results so far reproduced classically
- 4Need real molecule, verified energy
- 5Classical methods keep improving
Definition of success. (1) A chemically meaningful Hamiltonian (not a construct), (2) energy to 1.6 mHa, (3) a classical baseline from an independent group that cannot reach this accuracy under comparable resources, and (4) a verification path that does not rely on trusting the quantum device.
Built from
earlier problems → this oneThe problems this one is built from: progress or tools it needs (builds on), special cases that come first (generalizes), and weaker results on the way (implies). On the right, what builds on it.
- Start with
- Converged reference interaction energies for 100-atom noncovalent complexes: reconciling CCSD(T) and diffusion Monte CarloComputational Chemistry · D40
- Neural-network wavefunctions at chemical accuracy for 100+ electron molecules with transferable, amortised trainingComputational Chemistry · D54
- Efficient initial states for quantum phase estimation: overlap that classical heuristics cannot matchComputational Chemistry · D59.5
- Step 2
- A transferable exchange–correlation functional free of delocalization and self-interaction errorComputational Chemistry · D72
- Step 3
- Chemical accuracy for open-shell transition-metal complexes at polynomial cost without a hand-chosen active spaceComputational Chemistry · D66
- Step 4
Path to understanding
foundations → problemThe research entries this problem rests on, in the order to read them. Each links to its explainer.
- Start with
- Step 2
- Coupled-cluster theory and the CCSD(T) gold standardAlgorithm
- Quantum algorithmsAlgorithm
- Step 3
- Step 4
- Quantum computing for chemistryFrontier · host
- Then
- A verified quantum advantage for a chemically relevant ground-state energyThe problem
State of the art
- No such demonstration as of October 2026. Hardware results to date are classically reproducible. Robledo-Moreno et al. (Sci. Adv. 2025; IBM and RIKEN) combined quantum samples with classical diagonalisation (sample-based quantum diagonalisation) for an FeS cluster with a CAS(54,36) space on a 77-qubit device; energies were above those obtained by classical DMRG and selected CI. Legeza et al. (arXiv:2603.28648, preprint, 2026) report a high-accuracy classical ground-state energy for the same FeS CAS(54,36) model and CAS-SCF optimisation up to 89 electrons in 102 orbitals, a problem listed on the IBM and RIKEN Quantum Advantage Tracker.
Realistic applications
If real, quantum chemistry on fault-tolerant machines could supply reference energies for open-shell metal catalysts, enzymes and battery materials where classical methods are unreliable. If the classical frontier keeps advancing, the practical value shifts to polynomial speedups and dynamics.
What counts as solved
A peer-reviewed experiment on identified hardware with a specified molecule/Hamiltonian that satisfies both numbered criteria, with the classical baseline set by an independent group under a stated compute budget, and an independent verification of the quantum result.
How it gets verified
ReproductionA training run, experiment or computation rerun by someone else.
A peer-reviewed experiment on identified hardware for a specified molecule and Hamiltonian must satisfy both numbered criteria, with the classical baseline set by an independent group under a stated compute budget and the quantum result verified independently.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
Error-corrected hardware and compilation dominate, with moving classical baselines requiring theory.
Bottlenecks
ranked by votes- #1EngineeringFault-tolerant hardware at the required logical scale
Chemistry circuits need thousands of logical qubits and billions of gates.
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Connected problems
Progress
- Mar 30, 2026Classical Fe4S4 CAS(54,36) benchmark (preprint)source
Legeza et al. report high-accuracy classical results for a tracker-listed instance.
- Mar 3, 2026Improvement over selected CI on a constructed Hamiltonian (preprint)source
Kirby et al. report a quantum algorithm outperforming selected CI for a sparse-ground-state Hamiltonian.
- Jan 1, 2025Sample-based diagonalisation of Fe4S4 (77 qubits)source
IBM and RIKEN report a CAS(54,36) calculation combining quantum samples and classical diagonalisation (date given as year of publication).
- Apr 5, 2023Evidence for advantage questionedsource
Lee et al. publish analysis of state preparation and classical heuristics (date approximate).
- Nov 1, 2021THC resource estimate