Co-Designing Error Mitigation and Error Detection for Logical Qubits

Rohan S. Kumar, Takahiro Tsunoda, Sophia H. Xue, Dantong Li, Robert J. Schoelkopf, Yongshan Ding (Apr 23 2026).

Abstract: Near-term quantum workloads demand error management, yet the two lightest-weight techniques, Quantum Error Detection (QED) and Probabilistic Error Cancellation (PEC), have complementary cost profiles whose joint architectural design space remains unexplored. QED encodes logical qubits and discards error-flagged runs, filtering noise with low qubit overhead but leaving residual errors; PEC can correct these in software, but at exponential cost in noise strength. If QED efficiently reduces per-gate noise, PEC's cost savings can outweigh QED's discard overhead; realizing this, however, requires solving two system-level design challenges. First, the \textitQED interval -- how often detection cycles are inserted -- is a tunable architectural parameter governing the cost-accuracy tradeoff. We derive an efficiency condition and show that the canonical one-cycle-per-gate frequency does not achieve break-even in any code we evaluate, while optimized intervals on high-rate Iceberg codes do. Second, we discover that naive PEC+QED integration \textitdegrades accuracy below the QED-only baseline. The root cause is a transient error profile in the first detection cycle that corrupts PEC's noise model. We develop \textitsteady-state extraction, a co-designed characterization protocol that isolates steady-state error behavior, reducing estimation bias by up to $10.2\times$. On a $[[6,4,2]]$ Iceberg code running QAOA ($p{=}4$--$8$) with a fixed shot budget, PEC+QED achieves $2$--$11\times$ lower absolute error and up to $31\times$ lower MSE versus PEC on physical qubits, with per-interval savings compounding over interval depth.

Arxiv: https://arxiv.org/abs/2604.19871