Expressibility, Noise, and Error Mitigation in VQE Ansatz Selection
2026-06-03 • Emerging Technologies
Emerging Technologies
AI summaryⓘ
The authors investigate how well a measure called expressibility predicts the performance of quantum circuits used in a quantum computing method called VQE, which helps find molecular energies. They study two molecules under ideal, noisy, and error-mitigated conditions and find that expressibility's ability to predict performance breaks down under noise and different error corrections. Some simpler circuit features, like the number of two-qubit gates, sometimes work better for predicting errors than expressibility. Overall, their work suggests that common assumptions about choosing good quantum circuits need more careful validation under realistic noisy scenarios.
Variational Quantum Eigensolver (VQE)Quantum ChemistryAnsatz CircuitExpressibilityHilbert SpaceNoise in Quantum ComputingError MitigationZero-Noise Extrapolation (ZNE)Probabilistic Error Cancellation (PEC)Circuit Topology
Authors
Peter Annis, Abe Kassem, Evan Coleman
Abstract
The variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum chemistry applications, but selecting optimal ansatz circuits remains challenging. Expressibility, a metric quantifying a circuit's ability to explore the Hilbert space, has been proposed as a guide for ansatz selection, but recent work showed it inconsistently predicts VQE performance under realistic noise for $H_2$. We extend this investigation to cover both $H_2$ and $H_3^+$ under four execution scenarios: ideal, noisy, and noisy with zero-noise extrapolation (ZNE) or probabilistic error cancellation (PEC). We find that error mitigation does not reliably restore expressibility's predictive power. ZNE reduces error for only 4 of 12 $H_2$ circuits and 4 of 6 $H_3^+$ circuits, while PEC actually increases error in 11 of 12 $H_2$ circuits and all 6 $H_3^+$ circuits. We reproduce and extend Saib et al.'s key finding that circuit rankings scramble under noise (Spearman $ρ\approx -0.1$ between ideal and noisy rankings), and identify a new result: ZNE largely preserves noisy rankings ($ρ= +0.80$ for $H_2$) while PEC actively reorders them ($ρ= -0.22$). Noisy expressibility, computed from density matrix simulations, strongly predicts unmitigated performance for $H_3^+$ (Pearson $r = +0.91$, $p = 0.01$), but this metric is computationally intractable at scale. We demonstrate that zero-cost circuit topology metrics such as two-qubit gate count provide comparable or superior predictive power for PEC degradation ($r = +0.96$ for $H_3^+$), while standard expressibility best predicts noisy and ZNE performance for $H_2$ ($r = +0.74$ and $r = +0.77$).