Deep Learning Approaches to Quantum Error Mitigation

TL;DR

The paper tackles quantum error mitigation by training deep learning models to map noisy circuit output distributions to their ideal counterparts. It compares a wide range of architectures, with attention-based sequence-to-sequence models and the Perceiver emerging as the strongest performers, particularly after pretraining on simulated data and fine-tuning on real hardware. A large, diverse dataset from both simulated and real IBM QPUs enables robust benchmarking, including cross-dataset and cross-device transfer tests. The findings suggest data-driven QEM can rival or surpass standard baselines on realistic hardware, while also outlining scalability challenges and avenues for future work such as online learning and heterogeneous-model ensembles.

Abstract

We present a systematic investigation of deep learning methods applied to quantum error mitigation of noisy output probability distributions from measured quantum circuits. We compare different architectures, from fully connected neural networks to transformers, and we test different design/training modalities, identifying sequence-to-sequence, attention-based models as the most effective on our datasets. These models consistently produce mitigated distributions that are closer to the ideal outputs when tested on both simulated and real device data obtained from IBM superconducting quantum processing units (QPU) up to five qubits. Across several different circuit depths, our approach outperforms other baseline error mitigation techniques. We perform a series of ablation studies to examine: how different input features (circuit, device properties, noisy output statistics) affect performance; cross-dataset generalization across circuit families; and transfer learning to a different IBM QPU. We observe that generalization performance across similar devices with the same architecture works effectively, without needing to fully retrain models.

Figures (22)

• Figure 1: Device properties used as an input feature $\textbf{B}$ for our models. Densities are normalised across backend instances and include temporal variations in calibration data between periodic circuit executions.
• Figure 2: Noise and signal as a function of the number of layers in the circuit for ibm_algiers data.
• Figure 3: Scatter plots of signalagainst the number of layers for ibm_algiers data. The signal value is divided into six equally-spaced bins, whose edges are represented by dashed gray lines. Here we plot 10,000 points randomly sampled from each test dataset.
• Figure 4: ML pipeline for mitigating errors in a quantum circuit's output probability distribution.
• Figure 5: Example hyperparameter searches for two models for the Random Simulated dataset for ibm_algiers. Best and worst configurations in the search. The losses on the validation set during the runs are labelled by the trial index, given by the order they occurred during the procedure.