Demonstrating quantum error mitigation on logical qubits (2501.09079v1)

Abstract: A long-standing challenge in quantum computing is developing technologies to overcome the inevitable noise in qubits. To enable meaningful applications in the early stages of fault-tolerant quantum computing, devising methods to suppress post-correction logical failures is becoming increasingly crucial. In this work, we propose and experimentally demonstrate the application of zero-noise extrapolation, a practical quantum error mitigation technique, to error correction circuits on state-of-the-art superconducting processors. By amplifying the noise on physical qubits, the circuits yield outcomes that exhibit a predictable dependence on noise strength, following a polynomial function determined by the code distance. This property enables the effective application of polynomial extrapolation to mitigate logical errors. Our experiments demonstrate a universal reduction in logical errors across various quantum circuits, including fault-tolerant circuits of repetition and surface codes. We observe a favorable performance in multi-round error correction circuits, indicating that this method remains effective when the circuit depth increases. These results advance the frontier of quantum error suppression technologies, opening a practical way to achieve reliable quantum computing in the early fault-tolerant era.

• The paper demonstrates quantum error mitigation on logical qubits by applying zero-noise extrapolation (ZNE) with polynomial extrapolation to reduce logical errors in quantum error correction circuits.
• The research experimentally achieves a significant reduction in logical errors, reaching a post-mitigation residual error of approximately 1 x 10^-4 for a distance-7 code with minimal overhead.
• This method offers a scalable solution for enhancing quantum computation fidelity in the NISQ-to-FTQC transition era, applicable across various quantum error correction schemes and complexities.

Demonstrating Quantum Error Mitigation on Logical Qubits

The paper "Demonstrating quantum error mitigation on logical qubits" addresses a critical challenge in quantum computing: mitigating the errors that inevitably arise in quantum computations. The authors propose and experimentally demonstrate a practical application of zero-noise extrapolation (ZNE) to reduce logical errors in quantum error correction circuits. This research is significant as it presents a feasible path towards enhancing the fidelity of quantum computations, particularly during the crucial transitional phase from the era of noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing (FTQC).

A core aspect of the paper is the integration of ZNE with error correction techniques on cutting-edge superconducting processors. The approach presented involves deliberately amplifying the noise on physical qubits to predictably influence the circuit outcomes based on the noise strength, which is modeled as a polynomial function. This prediction allows for the effective application of polynomial extrapolation, mitigating logical errors with demonstrated efficacy across various quantum circuits, including repetition and surface codes. Notably, the method shows resilience in multiround error correction circuits, indicating robustness even as circuit depth increases.

The experimental demonstration includes two superconducting quantum processors used to assess error mitigation in quantum error correction circuits. These processors contain arrays of superconducting qubits with high-fidelity gates and excellent coherence properties, crucial for accurate quantum error correction. The implementation on these platforms confirms the applicability and effectiveness of the ZNE method. The authors employ various error injection strategies and validate the results through numerical simulations, showing close agreement with experimental outcomes.

One of the strongest numerical results highlighted is the significant reduction in logical errors achieved through the combination of ZNE and error correction. For example, in a distance-7 repetition code, the post-mitigation residual error is reduced to approximately $1 \times 10^{-4}$ with a modest sampling overhead of just 5. The experiments also affirm the scalability of the approach, as demonstrated by the universal reduction of logical errors across circuits of varying complexities.

From a theoretical standpoint, this work also presents a detailed analysis of the polynomial expression of circuit outcomes as a function of noise strength, providing a robust foundation for selecting appropriate extrapolation functions. This analysis is crucial for ensuring the method's effectiveness across different quantum error correction schemes.

The implications of this research are substantial. Practically, this method bridges the gap between current quantum technologies and the requirements for FTQC. It offers a scalable error mitigation solution that can be applied to logical circuits of significant complexity without excessive overhead. Theoretically, these findings enrich the understanding of error behavior in quantum circuits and offer a path forward for incorporating error mitigation with error correction.

Looking ahead, the paper speculates about future developments in AI and quantum computing. As quantum technologies advance, methods such as those demonstrated in this paper will be pivotal in enabling practical quantum applications. Continued improvements in qubit fidelity, coupled with sophisticated error suppression techniques, will facilitate the execution of larger and more complex quantum algorithms, ultimately paving the way toward realizing the full potential of quantum computing.

In conclusion, this research provides a comprehensive framework for quantum error mitigation, presenting a promising advancement in achieving reliable quantum computations in the early fault-tolerant era. The experimental and theoretical insights gained from this paper will inform future approaches to error suppression in quantum computing, contributing to the ongoing pursuit of practical and robust quantum technologies.