2026
Preprint
Logical qubits
Co-Designing Error Mitigation and Error Detection for Logical Qubits
Detection and mitigation.
Designed together.
The example is described below.
Error cancellation changes which operations are sampled and how their results are weighted. Error checks reject flagged runs. The final estimate combines the accepted results.
A concept view of the workflow. It does not simulate a new noise process. Compare the paper’s reported results below.
Design the two methods together.
Choose detection intervals and characterize residual noise to combine error detection with probabilistic error cancellation.
How the method works.
Error detection rejects a run when a check fails. Error mitigation reduces error in an estimate, but can increase its sampling uncertainty. A useful comparison must include both accuracy and uncertainty at the same number of attempted runs.
The paper designs the two steps together. It chooses when to check for errors, then models the noise left in the accepted runs. Probabilistic error cancellation uses that model to correct the estimate.
For example, Table II reports a simulation of the quantum approximate optimization algorithm (QAOA). At depth 8, it uses 100,000 attempted runs. Cancellation alone gives an absolute endpoint error of 0.00021 and a standard error of 0.0055. The combined method gives 0.00009 and 0.0013. The endpoint error is the distance from the ideal value. The standard error describes sampling uncertainty. A small endpoint error alone does not show how uncertain the estimate is.
The tool compares these reported simulation endpoints. They are finite-shot results, not forecasts for a different run count. See Table II and the preprint for the noise model, detection schedule and benchmark conditions.
One budget.
Four methods.
Compare endpoint error and uncertainty at the same 100,000 attempted shots.
Reported simulation endpoints. Both axes use logarithmic scales and MaxCut cost units. Marks are not probability distributions.
Selected / PEC + QED
Reported MSE
- Endpoint absolute error
- Standard error
- QED acceptance
- PEC norm γ
Same depth. Exact printed values.
Reported simulation endpoints at 100,000 attempted shots. Values retain the paper’s printed precision.
| Method | Abs. error | SE | MSE | γ | Acceptance |
|---|
Absolute error is the deviation of this finite-shot estimate from the ideal cost. It is not an independently measured true-bias floor. Reported MSE is preserved; rounded columns need not reproduce it exactly.
Read Table II and its method ↗Error detection filters runs. Probabilistic error cancellation changes the estimator and its sampling cost. The paper studies how to combine them.
Methods, scope and source
QED means quantum error detection. PEC means probabilistic error cancellation. QED-only and PEC + QED use the [[6,4,2]] Iceberg code with four logical qubits. PEC-only uses physical qubits. The study uses the paper’s QAOA MaxCut instance and depolarizing noise: one-qubit error 10−4, two-qubit error 10−3.
The two detection checks occur at the midpoint and end. The reported depths 4, 6 and 8 correspond to detection intervals of 20, 30 and 40 layers. The comparison uses attempted shots; the accepted counts can differ.
The display selects published endpoints. It does not run a new simulation, estimate a new optimum or predict performance at another shot budget.
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. Preprint, 2026.
Sources &
citation.
arXiv
2026 · Preprint
arXiv:2604.19871 (2026) · Preprint
View the citation
@misc{logical-2026,
title = {{Co-Designing Error Mitigation and Error Detection for Logical Qubits}},
author = {Rohan S. Kumar and Takahiro Tsunoda and Sophia H. Xue and Dantong Li and Robert J. Schoelkopf and Yongshan Ding},
year = {2026},
eprint = {2604.19871},
archivePrefix = {arXiv},
primaryClass = {quant-ph},
url = {https://arxiv.org/abs/2604.19871}
}