Comment on "Recovering noise-free quantum observables"

Abstract: Zero-noise extrapolation (ZNE) stands as the most widespread quantum error mitigation technique in order to aim the recovery of noise-free expectation values of observables of interest by means of Noisy Intermediate-Scale Quantum (NISQ) machines. Recently, Otten and Gray proposed a multidimensional generalization of polynomial ZNE for systems where there is not a tunable global noise source [Phys. Rev. A \textbf{99,} 012338 (2019)]. Specifically, the authors refer to multiqubit systems where each of the qubits experiences several noise processes with different rates, i.e. a non-identically distributed noise model. The authors proposed a hypersurface method for mitigating such noise, which is technically correct. While effective, the proposed method presents an unbearable experiment repetition overhead, making it impractical, at least from the perspective of quantum computing. In this comment, we show that the traditional extrapolation techniques can be applied for such non-identically distributed noise setting consisted of many different noise sources, implying that the measurement overhead is reduced considerably. For doing so, we clarify what it is meant by a tunable global noise source in the context of ZNE, concept that we consider important to be clarified for a correct understanding about how and why these methods work.

• The paper reinterprets the 'tunable global noise source', allowing uniform noise amplification in multiqubit systems for effective zero-noise extrapolation.
• The methodology lowers experimental overhead by reducing the need for millions of noise configurations to just a few measurements.
• The approach offers a practical route to error mitigation in current quantum computing hardware, advancing near-term quantum applications.

Comment on "Recovering Noise-Free Quantum Observables"

Overview

The paper "Comment on 'Recovering Noise-Free Quantum Observables'" by Etxezarreta Martinez et al. presents a critical examination of the quantum error mitigation method proposed by Otten and Gray. The focus lies on the applicability of Zero-Noise Extrapolation (ZNE) to multiqubit systems with non-identically distributed noise sources. The authors argue for a reinterpretation of the concept of a "tunable global noise source," thereby enabling the application of traditional ZNE techniques to more complex noise models, which Otten and Gray had previously deemed impractical.

Key Discussion Points

The paper critically addresses the hypersurface method proposed by Otten and Gray, discussing its effectiveness and limitations. The original method, aimed at recovering noise-free observables from systems where each qubit experiences unique noise processes, requires a substantial, arguably prohibitive, overhead in experimental repetitions. This overhead, the authors argue, makes the method impractical for quantum computing applications.

Etxezarreta Martinez et al. provide an alternative by clarifying the notion of "tunable global noise source." Their argument hinges on the ability to uniformly amplify all noise sources affecting the qubits by the same factor, $G$. This reinterpretation allows existing ZNE techniques to be applicable, effectively simplifying the problem and reducing the associated overhead in measurements.

Interpretations and Implications

1. Interpretation of Global Noise Source: The authors redefine the concept from requiring a single dominant noise parameter to allowing all noise parameters in a system to be proportionately amplified. This subtle shift aligns with practical methods such as pulse stretching and Probabilistic Error Amplification (PEA), enabling the application of ZNE even in non-uniform noise environments.
2. Reduction in Overhead: By using the clarified definition of global noise, the polynomial fitting in ZNE can be applied directly to the noise amplification factor, reducing the need for excessive overhead. For instance, whereas the method by Otten and Gray might require over a million unique noise configurations for a 100-qubit processor with T1/T2 type noise, the approach advocated by Etxezarreta Martinez et al. would reduce this to a manageable four measurements, a substantial practical gain.
3. Practical Applications: The paper's approach provides a feasible path to error mitigation in multiqubit systems without the demanding infrastructure or time resources previously thought necessary. This advancement is crucial for near-term quantum computing, wherein error rates persist as a significant barrier to functional computations and applications.

Theoretical and Practical Implications

Theoretically, this comment pushes the boundaries of ZNE applicability, challenging existing notions and opening avenues for its implementation in more complex noise scenarios. Practically, the insights provided align well with current quantum hardware capabilities, rendering ZNE a more attractive option for noise mitigation even in realistic, large-scale quantum systems.

Future Directions

This work lays the groundwork for exploring more refined noise models and mitigation techniques that can be implemented with feasible resources. Future work could focus on:

• Developing adaptive methods that dynamically adjust noise amplification strategies depending on real-time feedback.
• Exploring scalable versions of this methodology in large quantum systems, where physical constraints and system asymmetries might introduce additional complexities.
• Investigating direct experimental implementations of these findings to benchmark performance improvements in quantum computational tasks.

In conclusion, this paper offers a compelling critique and significant expansion to the applicability of error mitigation techniques, presenting a methodologically sound way to approach noise in quantum computations with practical efficiency. This advance is poised to enhance the utility of current quantum technology significantly.