# Weakly Supervised Quantum Error Mitigation

arXiv: https://arxiv.org/abs/2609.25555 · HTML: https://mlsanity.com/paper/2609.25555/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Training Complex Models with Multi-Task Weak Supervision](https://mlsanity.com/paper/1810.02840/) (2018)
- [Fast and Three-rious: Speeding Up Weak Supervision with Triplet Methods](https://mlsanity.com/paper/2002.11955/) (2020)
- [WRENCH: A Comprehensive Benchmark for Weak Supervision](https://mlsanity.com/paper/2109.11377/) (2021)
- [Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing](https://mlsanity.com/paper/1406.3824/) (2014)
- [Learning the Structure of Generative Models without Labeled Data](https://mlsanity.com/paper/1703.00854/) (2017)
- [Machine Learning for Practical Quantum Error Mitigation](https://mlsanity.com/paper/2309.17368/) (2023)
- [Neural Error Mitigation of Near-Term Quantum Simulations](https://mlsanity.com/paper/2105.08086/) (2021)

## Abstract (arXiv)

Supervised approaches to quantum error mitigation learn a map from noisy circuit outputs to ideal ones, and therefore require the ideal outputs. Producing those ideal outputs demands noiseless classical simulation, whose cost grows exponentially with system size, so supervision is unavailable in exactly the regime where mitigation matters most. We ask whether cheap, individually unreliable signals drawn from circuit structure and hardware calibration can take the place of ideal labels. We assemble sixteen heuristic labeling functions (stabilizer and parity constraints, relaxation and readout characteristics, local depth, gate counts, and neighboring activity), reconcile their disagreements with a probabilistic label model, and read the resulting per-qubit error probabilities as a readout channel whose inverse mitigates the measured distribution. No ideal output enters the training path. On 147,000 five-qubit circuits executed on two IBM devices, the method removes 24.3% (Algiers) and 28.8% (Hanoi) of the Kullback-Leibler divergence to the ideal distribution, against 15.4% and 21.5% for the strongest published analytical baseline, a margin that holds on both devices and lies far outside its bootstrap interval. Supervised neural models trained on ideal distributions remain stronger where such labels exist, and we quantify that gap rather than setting it aside; the method's claim is to the regime where they do not, since the labels they require cannot be computed for the circuits mitigation is needed for. The codes will be released shortly.