Digital zero noise extrapolation for quantum error mitigation (2005.10921v2)

Abstract: Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. These are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.

• The paper introduces a unitary folding framework that digitally scales noise to extrapolate error-free quantum circuit outputs.
• The paper proposes parameter noise scaling to simulate calibration errors and adjust noise levels effectively in quantum gates.
• The paper validates its approach with empirical benchmarks on IBM Q processors, achieving error reductions up to 24 times.

Analysis of "Digital Zero Noise Extrapolation for Quantum Error Mitigation"

The paper "Digital Zero Noise Extrapolation for Quantum Error Mitigation," authored by Tudor Giurgica-Tiron et al., presents a comprehensive paper on enhancing zero-noise extrapolation (ZNE) techniques for error mitigation in quantum computations. ZNE is pivotal in the noisy intermediate-scale quantum (NISQ) era, addressing an exigent need to mitigate errors in quantum circuits without resorting to additional quantum resources. This paper provides detailed methodologies for applying ZNE digitally, primarily through noise scaling techniques and extrapolation methods, aiming to extend the applicability of ZNE for more complex quantum programs.

Key Contributions

1. Unitary Folding Framework: The paper introduces advancements in noise scaling through unitary folding. Unitary folding involves the modulation of circuit noise by virtually increasing the circuit depth using operations like circuit folding and gate folding. These methods replace a unitary operation with a sequence that effectively magnifies the noise, thus enabling the extrapolation of circuit results to zero noise. This approach allows users to scale noise digitally, utilizing only the quantum instruction set, making it applicable even when direct physical control over gate operations is not available.
2. Parameterized Noise Scaling: Another method introduced is parameter noise scaling aimed at handling noise models associated with calibration errors. This approach directly scales the noise by injecting artificial variability into the control parameters of quantum gates, effectively adjusting the perceived noise level during computations.
3. Extrapolation Methods: The authors explore both non-adaptive and adaptive extrapolation approaches. The polynomial and poly-exponential models are applied to infer zero-noise results from scaled noise levels. Notably, the adaptive extrapolation method demonstrated allows for real-time adjustments to the noise scaling process based on intermediate computational results, optimizing the sample usage for higher precision results.
4. Empirical Validation and Benchmarking: The paper provides extensive numerical simulations and empirical results from experiments conducted on IBM Q's London superconducting quantum processor. Robust improvements over traditional, non-mitigated executions are evident, with error reductions reaching up to 24 times over non-mitigated cases.

Practical and Theoretical Implications

From a practical perspective, the introduced methods significantly enhance the utility of ZNE for near-term quantum devices. By adopting a digital approach, these methods promise broader adoption and utility across various quantum computation platforms without requiring prohibitive access to low-level quantum hardware controls. The techniques are particularly beneficial for optimizing variational quantum algorithms like QAOA, demonstrating substantial improvements across realistic quantum tasks.

Theoretically, the paper enriches the framework for understanding noise scaling and extrapolation as a statistical inference problem, opening new avenues for research in both ZNE methodologies and noise modeling. The numeric and adaptive approaches to selecting scale factors and extrapolation orders represent a meaningful advancement in noise mitigation strategies, aligning computational complexity with desired error thresholds.

Speculation on Future AI Developments

The methodologies and insights presented in this paper pave the way for future developments in AI-driven quantum computing. Adaptive learning techniques could be integrated to automate ZNE processes, further optimizing quantum circuit execution based on historical performance data. Quantum algorithms themselves may evolve to intrinsically account for noise patterns, integrated with error mitigation as part of the computational logic.

In conclusion, "Digital Zero Noise Extrapolation for Quantum Error Mitigation" significantly contributes to the field of quantum error mitigation by broadening the applicability and effectiveness of ZNE techniques. By enabling practical error mitigation strategies through digital noise scaling and advanced extrapolation methods, this work equips quantum programmers with essential tools to navigate the NISQ landscape efficiently.