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QEM-Bench: Benchmarking Learning-based Quantum Error Mitigation and QEMFormer as a Multi-ranged Context Learning Baseline
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Introduces QEM-Bench, a 22-dataset benchmark for learning-based quantum error mitigation, and QEMFormer, a two-branch MLP + graph transformer model over circuit DAGs that outperforms baselines on it.
Problem
Learning-based quantum error mitigation lacks standardized datasets and consistent experimental settings, and existing ML-QEM encoders and architectures fail to capture circuit topology and both short- and long-range dependencies.
Approach
Encode quantum circuits as DAGs with gate-level, circuit-level and multi-Pauli-basis expectation features, and combine an MLP branch (short-range context) with a graph transformer branch (long-range and topological dependencies) to regress ideal expectation values; packaged with a 22-dataset benchmark.
Key results
- On standard random circuits with fake provider noise, QEMFormer reaches RMSE 0.054 vs. 0.063 for MLP and 0.080 for GNN.
- On Trotter-step zero-shot with incoherent noise, QEMFormer achieves RMSE 0.025, versus 0.313 for noisy inputs.
- On IBM Kyiv Pre (50 qubits), QEMFormer attains MAE 0.018 and RMSE 0.026, the lowest among compared methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use QEMFormer instead of the strongest listed baseline | QEM on standard random circuits · Random circuits, incoherent noise | RMSE: 0.063 ± 0.043 -> 0.087 ± 0.055 | Hurt |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard random circuits · Random circuits, coherent noise | RMSE: 0.096 ± 0.064 -> 0.095 ± 0.064 | Helped |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard random circuits · Random circuits, provider noise | RMSE: 0.059 ± 0.044 -> 0.054 ± 0.036 | Helped |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard QAOA circuits · QAOA, incoherent noise | RMSE: 0.054 ± 0.037 -> 0.054 ± 0.035 | No clear effect |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard QAOA circuits · QAOA, coherent noise | RMSE: 0.068 ± 0.043 -> 0.061 ± 0.039 | Helped |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard QAOA circuits · QAOA, provider noise | RMSE: 0.045 ± 0.030 -> 0.033 ± 0.021 | Helped |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard Trotter circuits · Trotter, incoherent noise | RMSE: 0.033 ± 0.023 -> 0.024 ± 0.015 | Helped |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard Trotter circuits · Trotter, coherent noise | RMSE: 0.190 ± 0.156 -> 0.189 ± 0.145 | Helped |
| Use QEMFormer instead of the strongest listed baseline | QEM on standard Trotter circuits · Trotter, provider noise | RMSE: 0.051 ± 0.033 -> 0.062 ± 0.041 | Hurt |
| Use QEMFormer rather than noisy expectation values | QEM on standard circuits · Random circuits, incoherent noise | RMSE: 0.192 ± 0.132 -> 0.087 ± 0.055 | Helped |
| Use QEMFormer rather than noisy expectation values | QEM on standard circuits · QAOA, provider noise | RMSE: 0.147 ± 0.072 -> 0.033 ± 0.021 | Helped |
| Use QEMFormer rather than noisy expectation values | QEM on standard circuits · Trotter, coherent noise | RMSE: 0.455 ± 0.217 -> 0.189 ± 0.145 | Helped |
Surprising findings
- Multiple implementations of ZNE, CDR and RF performed weakly on QAOA circuits and were excluded from mitigation results.
- On the Brisbane Raw dataset, the GNN and RF baselines were weaker than the noisy baseline in some metrics, and on Kyiv Raw all methods barely improve over noisy RMSE (about 0.22-0.24).
Limitations
- QAOA results for ZNE, CDR and RF were unreliable and excluded from mitigation comparisons.
- Large-scale real-device raw datasets show little improvement over noisy baselines for all methods.
- Benchmark is simulated noise for most settings; authors state the benchmark will be updated continuously.
Experimental setup
Datasets: QEM-Bench (22 datasets: Trotterized TFIM, random unstructured circuits, QAOA MaxCut, IBM Kyiv and Brisbane real-device d
Benchmarks: QEM-Bench standard settings QEM-Bench advanced zero-shot and unseen-observable settings QEM-Bench large-scale IBM Kyiv and Brisbane datasets
Metrics: RMSE MAE AE distribution STD
Baselines: MLP GNN OLS Random Forest ZNE CDR GTranQEM
Builds on: GTranQEM Clifford Data Regression Zero-Noise Extrapolation
Closest papers by meaning
- QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design (NeurIPS 2025 · similarity 0.86)
- TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search (NeurIPS 2025 · similarity 0.85)
- Training-Free Quantum Architecture Search (AAAI 2024 · similarity 0.85)
- MG-Net: Learn to Customize QAOA with Circuit Depth Awareness (NeurIPS 2024 · similarity 0.85)
- Q-MAML: Quantum Model-Agnostic Meta-Learning for Variational Quantum Algorithms (AAAI 2025 · similarity 0.85)
- Curriculum reinforcement learning for quantum architecture search under hardware errors (ICLR 2024 · similarity 0.85)
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