VULCAN (Variational Upbuilding, Layered Compression, Adaptive N‑body Perturbation) is a gradient‑free variant of the Variational Quantum Eigensolver that appends an entire operator pool as a single layer and then prunes it with overlap‑guided compression. The compression stage freezes all earlier layers while greedily inserting generators ranked by overlap gradients. The resulting ansatz is much shallower than the uncompressed version and allows state‑overlap measurements to replace expensive Hamiltonian gradients.

Using high‑performance emulation up to 32 logical qubits, the authors obtain chemical accuracy for hydrogen chains, BeH₂, H₂O, and the 32‑qubit C₃H₆ system. For the chains, the required measurement cost is only 5–20 % of the batched ADAPT‑VQE protocol that uses a qubit‑excitation–based (QEB) pool, and the CNOT counts decrease by about 35–90 %. In the C₃H₆ case, a single VULCAN layer combined with a GPU‑accelerated stochastic Epstein–Nesbet (ENPT²) correction reaches chemical accuracy at a measurement cost of only approximately 0.02 % of the batched ADAPT‑VQE baseline.

These efficiencies stem from three complementary techniques. First, VULCAN uses a linearly scaling minimal complete pool that is 4–12 times smaller than the QEB pool, eliminating the need for Hamiltonian gradient measurements. Second, the grow‑then‑compress routine reduces circuit depth after each layer is added. Third, the ENPT² post‑processing provides an early stopping criterion that guarantees chemical accuracy even when the bare VULCAN ansatz does not.

The reported benchmarks were performed on emulators that simulate logical qubits under ideal conditions; none of the results have yet been demonstrated on noisy intermediate‑scale quantum devices. Moreover, the single‑Pauli generator pool does not explicitly conserve particle number or total spin, which can lead to spin contamination in strongly correlated regimes.