Orders of magnitude sampling overhead reduction in quantum error mitigation
Quantum error mitigation (QEM) infers noiseless expectation values from noisy variants of a target quantum circuit. Unlike quantum error correction, QEM requires no additional hardware resources and is therefore routinely employed in experiments on contemporary quantum processors. QEM strategies based on agnostic noise amplification (ANA) are intrinsically resilient to temporal noise drift during the execution of the experiment, but their sampling cost (runtime overhead) remains a major practical bottleneck. In this work, we introduce the virtual noise scaling framework and combine it with layered mitigation to further enhance performance. While virtual noise scaling consistently reduces sampling overhead, we identify a specific noise threshold for the layered mitigation approach. When the noise level is above this threshold, layered mitigation decreases the sampling overhead; conversely, when below it, the overhead increases. Notably, this threshold is circuit-independent and depends solely on the number of layers. For strong noise, the combination of virtual noise scaling and layered mitigation yields several orders of magnitude reduction in sampling overhead compared with conventional zero-noise extrapolation post-processing. As a result, mitigation tasks that once seemed unrealistic are now challenging but achievable. The proposed approach is compatible with dynamic circuits and can be seamlessly integrated with error detection and quantum error correction schemes. In addition, it is also applicable to ANA-based mitigation of mid-circuit measurements and preparation errors. Our findings extend to any constant-step amplification factors and therefore also apply to probabilistic error amplification (PEA) QEM. We validate our post-processing approach by applying it to previously reported experimental data, where we observe a substantial improvement in mitigation efficiency and accuracy.