Optimization of Richardson extrapolation for quantum error mitigation

Quantum error mitigation is a key concept for the development of practical applications based on current noisy intermediate-scale quantum devices. One of the most promising methods is Richardson extrapolation to the zero noise limit. While its main idea is rather simple, the full potential of Richardson extrapolation has not been completely uncovered yet. We give an in-depth analysis of the relevant parameters of Richardson extrapolation and propose an optimized protocol for its implementation. This protocol allows for a precise control of the increase in statistical uncertainty and lays the foundation for a significant improvement of the mitigation performance achieved by increasing the number of nodes. Furthermore, we present a set of nodes that, on average, outperforms the linear, exponential, or Chebyshev nodes frequently used for Richardson extrapolation without requiring any additional resources.