Optimality of SALEM among syndrome-based LEM methods

Determine whether syndrome-aware logical error mitigation (SALEM) achieves optimal efficiency among all logical error mitigation protocols that exploit error-correction syndrome information, i.e., ascertain whether any syndrome-based logical error mitigation method can surpass SALEM in shot overhead required to produce unbiased estimates of logical circuit observables.

Background

The paper introduces SALEM, a syndrome-aware logical error mitigation strategy that leverages syndrome information measured during error correction to substantially reduce the shot overhead compared to external logical error mitigation (ExtLEM). The authors show that SALEM can outperform approaches that do not use syndrome information and define new thresholds where SALEM becomes advantageous relative to physical error mitigation.

Despite these advances, it remains unresolved whether SALEM is the best possible use of syndrome data for logical error mitigation. Establishing the optimality of SALEM would determine whether further improvements are possible or whether SALEM already achieves the minimal feasible overhead among syndrome-based methods, a question with direct practical impact on resource estimates for error-corrected quantum computation.