Optimization of Richardson extrapolation for quantum error mitigation

Abstract

Quantum error mitigation is a key concept for the development of practical applications based on current noisy intermediate scale quantum (NISQ) 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 novel set of nodes that, on average, outperforms the linear, exponential or Chebyshev nodes frequently used for Richardson extrapolation without requiring any additional resources.

11 pages, 9 figures

References in corpus (4)

• Surface codes: Towards practical large-scale quantum computation
• Extending quantum probabilistic error cancellation by noise scaling
• Experimental characterisation of a non-Markovian quantum process
• Analyzing the impact of time-correlated noise on zero-noise extrapolation

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• Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation
• A Useful Metric for the NISQ Era: Qubit Error Probability and Its Role in Zero Noise Extrapolation
• Error-Mitigated Multi-Layer Quantum Routing