Co-Designing Error Mitigation and Error Detection for Logical Qubits

Quantum Physics [Submitted on 21 Apr 2026] 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 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. Comments: 15 pages, 9 figures, 2 tables Subjects: Quantum Physics (quant-ph); Hardware Architecture (cs.AR) Cite as: arXiv:2604.19871 [quant-ph]   (or arXiv:2604.19871v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.19871 Focus to learn more Submission history From: Rohan Kumar [view email] [v1] Tue, 21 Apr 2026 18:00:02 UTC (3,372 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.AR References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)