Error Mitigation Thresholds in Noisy Random Quantum Circuits

Area of Science:

• Quantum Computing
• Quantum Information Science
• Computational Physics

Background:

• Near-term quantum simulations are susceptible to noise, necessitating error mitigation strategies.
• Effective error mitigation often depends on precise characterization of noise sources.
• Probabilistic error cancellation and tensor network methods are key strategies for mitigating errors.

Purpose of the Study:

• To investigate the robustness of quantum error mitigation techniques when noise is imperfectly characterized.
• To determine the impact of noise characterization errors on probabilistic error cancellation and tensor network methods.
• To analyze the theoretical limits of error mitigation in different spatial dimensions.

Main Methods:

• Adaptation of the Imry-Ma argument to analyze noise robustness.
• Study of random spatially local circuits in D >= 2 and 1D.
• Theoretical prediction of a threshold in robustness for D >= 2.

Main Results:

• A threshold in robustness exists for error mitigation in D >= 2 spatial dimensions, allowing for longer mitigation times with imperfect noise characterization below the threshold.
• In 1D circuits, error mitigation fails rapidly (at O(1) time) with any noise characterization imperfection.
• Error mitigation is practical only for noise that is sufficiently well-characterized.

Conclusions:

• The practical applicability of quantum error mitigation is highly dependent on the accuracy of noise characterization.
• Findings have implications for quantum advantage experiments, quantum phase transition studies, and near-term quantum algorithms.
• Robustness analysis provides critical insights into the limitations and potential of current quantum computing technologies.