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 \(\ce {H2}\). We extend this investigation to cover both \(\ce {H2}\) and \(\ce {H3+}\) 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 \(\ce {H2}\) circuits and 4 of 6 \(\ce {H3+}\) circuits, while PEC actually increases error in 11 of 12 \(\ce {H2}\) circuits and all 6 \(\ce {H3+}\) circuits. We reproduce and extend Saib et al.’s key finding that circuit rankings scramble under noise (Spearman ρ ≈ −0.1 between ideal and noisy rankings), and identify a new result: ZNE largely preserves noisy rankings (ρ = +0.80 for \(\ce {H2}\)) while PEC actively reorders them (ρ = −0.22). Noisy expressibility, computed from density matrix simulations, strongly predicts unmitigated performance for \(\ce {H3+}\) (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 \(\ce {H3+}\)), while standard expressibility best predicts noisy and ZNE performance for \(\ce {H2}\) (r = +0.74 and r = +0.77).

Asynchronous iterative methods tolerate straggling processors by allowing workers to proceed with stale data, but at a cost: the iterates become inconsistent, potentially degrading convergence. We investigate whether convergence accelerators such as Anderson acceleration compensate for this degradation. We experimentally study three fixed-point iterations: the Jacobi method for sparse linear systems, value iteration for the Bellman equation, and the Hartree–Fock self-consistent field (SCF) iteration. The experiments are conducted using a high-performance execution framework, Ray, which abstracts the complexity of distributed systems and enables code parallelization and fault injection with minimal changes.

This study seeks to understand the soft error vulnerability of asynchronous iterative methods, with a focus on stationary iterative solvers such as Jacobi. The implementations make use of hybrid parallelism where the computational work is distributed over multiple nodes using MPI and parallelized on each node using openMP. A series of experiments is conducted to measure the impact of an undetected soft fault on an asynchronous iterative method, and to compare and contrast several techniques for simulating the occurrence of a fault and then recovering from the effects of the faults. The data shows that the two numerical soft-fault models tested here more consistently than a “bit-flip” model produce bad enough behavior to test a variety of recovery strategies, such as those based on partial checkpointing.