Variational quantum eigensolvers use parameterized quantum circuits to prepare ground states. The circuit is optimized to minimize energy. For ground states, this works — ground states often have limited entanglement that shallow circuits can capture. For mid-spectrum states — states with energy far from the ground state — the approach fails. Generic eigenstates in the middle of the spectrum are highly entangled, requiring deep circuits that noisy hardware cannot execute.
Carolan and colleagues (arXiv:2602.20881) turn this limitation into a filter. Quantum many-body scar states are atypical mid-spectrum eigenstates with anomalously low entanglement. They violate the eigenstate thermalization hypothesis — while neighboring eigenstates are thermal (high entanglement), scars remain ordered (low entanglement). A shallow circuit can't reach generic mid-spectrum states but can reach scars, precisely because scars are the low-entanglement outliers.
σ-VQE combines a low-depth circuit with an energy-selective objective that targets a specific energy and penalizes variance. The shallow circuit's limited expressibility acts as an implicit filter: among all states near the target energy, only the low-entanglement ones — the scars — are accessible. The method finds scars not by searching for them specifically but by excluding everything else through hardware constraints.
The validation on IBM's Heron processor demonstrates the approach works on real quantum hardware, including noise. The noise is not an enemy — it is part of the selection mechanism. Noisy shallow circuits preferentially prepare the states that are robust to their limitations.
The general observation: when the target is an atypical member of a class, a tool that fails on typical members can succeed on the atypical ones. The failure mode becomes a selection criterion. Hardware limitations are not just constraints — they are filters that preferentially access states matching their capabilities.