Quantum Error Mitigation (2210.00921v3)

Abstract: For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of `NISQ' machines we must seek to mitigate errors rather than completely remove them. This review surveys the diverse methods that have been proposed for quantum error mitigation, assesses their in-principle efficacy, and then describes the hardware demonstrations achieved to date. We identify the commonalities and limitations among the methods, noting how mitigation methods can be chosen according to the primary type of noise present, including algorithmic errors. Open problems in the field are identified and we discuss the prospects for realising mitigation-based devices that can deliver quantum advantage with an impact on science and business.

• The paper categorizes diverse error mitigation techniques for NISQ devices, including zero-noise extrapolation and probabilistic error cancellation.
• It evaluates these methods through empirical analyses that demonstrate enhanced fidelity in quantum simulations without extensive qubit overhead.
• The work outlines pathways for integrating mitigation techniques into scalable quantum computing and inspires future hybrid mitigation-correction frameworks.

Quantum Error Mitigation: A Comprehensive Review

Overview

The paper "Quantum Error Mitigation" presents an in-depth review of the strategies and methodologies implemented to address the challenge of noise in quantum computing, specifically during the era of Noisy Intermediate-Scale Quantum (NISQ) devices. The authors, led by Zhenyu Cai and a team of experts in quantum computing, provide a detailed analysis and categorization of error mitigation techniques, evaluate their impact through empirical results, and explore their potential to enhance the utility of quantum computers in various applications.

Quantum Error Mitigation Strategies

In the context of quantum computing, error mitigation has emerged as a crucial approach due to the prohibitive qubit overheads and technical challenges associated with full-scale quantum error correction. The paper categorizes the techniques into different types based on their underlying principles and applications:

1. Zero-Noise Extrapolation (ZNE): This approach leverages the idea of extrapolating the expectation values of quantum circuits run at multiple noise levels towards a zero-noise setting. Methods for noise scaling include both pulse stretching and gate insertion, allowing for practical implementation on existing hardware.
2. Probabilistic Error Cancellation (PEC): By using quasi-probability decomposition, PEC constructs an unbiased estimator of the noise-free expectation value through a combination of noisy experiments. While this method can achieve zero bias, it suffers from an exponential scaling in sampling overhead.
3. Measurement Error Mitigation: Addressing errors in state preparation and measurement (SPAM), this method leverages classical post-processing of measurement assignments to correct erroneous measurement statistics, often using techniques like matrix inversion or partial tomography.
4. Symmetry Constraints: Utilizing the inherent symmetries of quantum systems, this method post-processes results by verifying symmetries, thereby discarding results that do not obey expected conservation laws, which improves accuracy in expectation value estimates.
5. Purity Constraints and Virtual Distillation: These techniques aim to reduce decoherence effects by approximating the ideal pure state closest to the noisy state. Virtual distillation achieves this by strategically using multiple copies of quantum states to project onto the dominant eigenvector.
6. Subspace Expansions: This methodology employs knowledge about the quantum state to constrain the problem to a lower-dimensional subspace, optimizing the performance within this expanded subspace using classical post-processing.
7. N-representability: Especially relevant in quantum chemistry, this seeks to ensure that the reduced density matrices are representative of an N-body quantum state, applying constraints from quantum chemistry to refine outcomes.
8. Learning-Based Methods: These approaches incorporate machine learning and other data-driven techniques to understand and mitigate noise using classically simulable circuits, offering a broader and adaptive framework for error characterisation.

Implications and Future Developments

The paper underscores that while error mitigation does not replace the need for full error correction, it significantly extends the applicability and capability of NISQ devices. By effectively reducing the impact of noise, error mitigation techniques can enhance the fidelity of quantum simulations and computations without the qubit and gate overheads inherent in traditional error correction.

From a theoretical perspective, these methods provide insight into the structure of quantum states and the impact of noise, facilitating the development of more robust algorithms. Practically, the implementations highlighted within the survey provide a foundation for scaling quantum experiments in current quantum hardware, demonstrating the potential to surpass classical algorithms' performance even in the pre-fault tolerant era.

As quantum technology progresses, these methods could be pivotal in bridging the gap towards fully fault-tolerant quantum computing. Future research may focus on optimizing these techniques, exploring hybrid error mitigation-error correction frameworks, and tailoring them for specific applications in quantum simulation, cryptography, and beyond.

The paper presented a comprehensive discussion on the state-of-the-art in quantum error mitigation, providing valuable insights into existing methods, their application potential, and the pathway towards scalable quantum computing solutions.