Finding the ground-state energy of a molecule is one of the problems quantum computers are meant to be good at. The hard part is not running a circuit but choosing which one: the circuit has to be short enough to survive today's noisy hardware and expressive enough to reach the right state. For the Mitsubishi Chemical Group and AIST challenge at GIC 2026, our team, Ryoushi / Quantum Buddies, built H-cGQE to learn that choice from the molecule itself.
\nThis write-up covers what we built, what the results show, and where they are weaker than they first look.
\nThe generative quantum eigensolver (GQE; Nakaji et al., arXiv:2401.09253) treats circuit design as sequence generation. A Transformer writes a circuit one operator at a time, choosing each from a fixed pool, and it is trained so that circuits with lower energy become more likely. It is the same trick a language model uses, with gates in place of words.
\nPlain GQE learns one molecule at a time. H-cGQE, the Hamiltonian-conditioned GQE, feeds the molecule's Hamiltonian into the model, so one network can propose circuits for many molecules:
\nThe model is small, about 7.7 million parameters (256-dimensional, 8 heads, 4 layers). The operator pool is the set of UCCSD excitations, mapped to qubits with the Jordan–Wigner transform. It grows fast with molecule size: 192 entries for H₂ on 4 qubits, 1,408 for LiH on 12, 3,456 for BeH₂ on 14 and 11,088 for N₂ on 20.
\nWe also built a chemical graph neural network, three layers of message passing over the molecule's bonds. In the final code it conditions a CUDA-Q GQE baseline, not the H-cGQE model itself.
\n","Training has two stages.
\nThe reward is mostly energy, with smaller terms for entanglement (0.1), circuit depth (0.05), commuting structure (0.05) and diversity (0.2). An optional quality-diversity mode, QD-GRPO, keeps a MAP-Elites archive: a 10 × 10 grid over entanglement density and circuit depth that holds the best circuit found in each cell. It adds a novelty bonus that decays from 1.0 to 0.1 over training, so early exploration gives way to exploitation.
\nEach proposed circuit still needs its rotation angles. L-BFGS-B tunes them, cheaply during training (three to five iterations) and fully for evaluation (200 iterations, tolerance 10⁻¹⁰). Simulation ran on CUDA-Q, on NVIDIA L40S GPUs on the AIRE cluster and B200s through qBraid, behind a cache of more than 24,000 computed energies.
\nOur headline number is 0.63 mHa: the error of the H-cGQE circuit for methyl iodide in an 8-qubit active space (four electrons in four orbitals, STO-3G basis), measured against the exact answer in that space. Chemical accuracy is usually taken as 1.6 mHa, so on its face this clears the bar.
\nThree details matter.
\nXYYX term, and its optimised angle is 0.000244, almost zero.The hardware-efficient VQE baseline, a generic circuit with no chemistry in it, was 987.8 mHa out. That gap is real, and it is the clearest evidence that chemically structured circuits matter.
\nThe 0.63 mHa run also came from a checkpoint trained with REINFORCE on energy rewards, not from the DAPO or QD-GRPO training described above.
\nOur own ablation says: mostly not yet. Compared with the supervised model alone, reinforcement learning took H₂ from 20.52 mHa to 0.15. On every larger molecule it made things slightly worse.
\n| Molecule | \nAfter fine-tuning (mHa) | \nAfter RL (mHa) | \n
|---|---|---|
| H₂ | \n20.52 | \n0.15 | \n
| LiH | \n1.81 | \n1.85 | \n
| BeH₂ | \n33.77 | \n34.81 | \n
| Methyl iodide (12 orbitals) | \n1.43 | \n1.59 | \n
| N₂ | \n126.56 | \n126.77 | \n
A later check suggests why. The cheap energy estimate used during training, with the angles held fixed, correlated only weakly with the fully optimised energy (Spearman 0.23, p = 0.42). The learning signal was mostly noise. Across the whole suite, 4 of the 17 molecules we benchmarked reached chemical accuracy in simulation.
\nWe ran selected circuits on hardware through qBraid.
\nWe also tried fragmenting a molecule so a 12-qubit problem could be solved with circuits of at most 8 qubits. In simulation the fragmentation cost 11.3 mHa. On hardware the error was about a hartree.
\nWe built a working end-to-end system: a Hamiltonian-conditioned circuit generator, a training pipeline with quality-diversity reinforcement learning, GPU simulation at scale, and runs on two hardware vendors with a third submitted. The engineering held up, and structured circuits beat a generic ansatz by a wide margin.
\nThe learning did not yet pay off beyond the smallest molecule. The headline result sits on a problem where Hartree–Fock is already accurate, and the next step is clear. We need a training signal that tracks the converged energy, and an evaluation on molecules the model has never seen. That held-out test is still open.
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