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This paper explores the co-design of Quantum Error Detection (QED) and Probabilistic Error Cancellation (PEC) for near-term quantum error mitigation. They identify that naive integration of QED and PEC degrades accuracy due to transient errors in the initial QED cycle, and address this with a novel "steady-state extraction" characterization protocol. Results on a [[6,4,2]] Iceberg code running QAOA show that co-designed PEC+QED achieves significant error reduction compared to PEC alone, demonstrating the benefits of optimized QED intervals and noise model characterization.
Combining quantum error detection with probabilistic error cancellation can backfire, but a co-designed approach unlocks up to 31x lower error in QAOA on a logical qubit.
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 \textit{QED 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 \textit{degrades} 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 \textit{steady-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.
