Error mitigation versus error correction in quantum computers

Short answer: Quantum error correction (QEC) aims to enable reliable, fault-tolerant quantum computation, while quantum error mitigation (QEM) offers practical techniques to reduce the effect of noise on today's noisy devices without QEC's significant hardware overhead. A 2023 review in Reviews of Modern Physics says that in the noisy intermediate-scale era one must seek to mitigate errors rather than completely eliminate them. Whether mitigation can deliver a useful quantum advantage is still an open research question.

What is the fundamental difference between mitigation and correction?

The distinction between quantum error mitigation (QEM) and quantum error correction (QEC) lies in their approach to noise and their resource demands. QEC extends classical error-correcting codes to enable reliable quantum computation and fault-tolerance, effectively aiming to eliminate errors. In contrast, QEM offers practical techniques to reduce noise effects in quantum devices without the significant hardware overhead required by QEC. The 2023 review says the theory of quantum fault tolerance can provide a long-term answer, but in the noisy intermediate-scale era one must seek to mitigate errors rather than completely eliminate them. That review surveys methods for QEM, assessing their in-principle efficacy and describing hardware demonstrations achieved to date. These methods are chosen based on the primary type of noise present, including algorithmic errors. The field continues to identify open problems and discuss the prospects for realizing mitigation-based devices that can deliver a quantum advantage.

How does error suppression differ from mitigation?

IBM's blog breaks error handling into three core pieces: error suppression, error mitigation, and error correction, though terminology within the field can be confusing and not totally defined. Error suppression is the most basic level of error handling, referring to techniques that use knowledge about undesirable effects to introduce customization that anticipates and avoids their potential impacts. IBM says these techniques operate at the closest level to the hardware, often unbeknownst to the user, and consist of altering or adding control signals to ensure the processor returns the desired result. Error mitigation, meanwhile, uses the outputs of ensembles to address noise. The differences between suppression and mitigation are subtle and not strictly defined, leading to disagreement about what exactly each term means. IBM is a vendor, so treat its framing as its own.

What are the mathematical challenges in noise inversion?

A key aspect of QEM is the invertibility of the noise. A 2025 paper examines the implications of noise invertibility for QEM, clarifying fundamental distinctions between QEC and QEM through intuitions built upon classical and quantum communication scenarios. When noise is not invertible, standard mathematical tools may fail. Specifically, the commonly used Moore-Penrose pseudoinverse may not be trace preserving, which is a critical property for quantum operations. To address this, an explicit construction called the Drazin-inverse has been proposed for non-invertible noise. This construction is trace preserving, making it suitable for quantum error mitigation tasks. Furthermore, the consequences of having imperfect knowledge about the noise have been studied. Conditions have been derived for when noise can be reduced using QEM despite this imperfect knowledge.

What are the limitations and open problems?

The 2023 review identifies commonalities, limitations and open problems among mitigation methods, and assesses their efficacy in principle and through hardware demonstrations to date. The choice of mitigation method depends on the primary type of noise present, including algorithmic errors, according to the review. While the prospects for realizing mitigation-based devices that can deliver a quantum advantage with an impact on science and business are discussed, these remain largely at the research stage. There is no claim of operational adoption or commercial deployment of these techniques for solving real-world problems at scale. The review describes noise as errors in elementary physical components caused by unwanted or imperfect interactions. Whether mitigation can consistently deliver a quantum advantage is an open question.

FAQ

What is quantum error correction?

It extends error-correcting codes to quantum computation to enable reliable computation and fault tolerance, according to a 2025 paper on error mitigation.

What is quantum error mitigation?

Practical techniques that reduce the effects of noise in quantum devices without the significant hardware overhead needed by error correction.

Where does error suppression fit?

IBM describes three pieces: suppression, mitigation and correction, and says the differences, especially between suppression and mitigation, are subtle and not totally defined. IBM says suppression works closest to the hardware by altering or adding control signals.

Why mitigate instead of correct?

The 2023 review says fault tolerance can answer the noise problem in the long term, but in the coming era of noisy intermediate-scale machines one must seek to mitigate errors rather than completely eliminate them.

Can mitigation deliver a quantum advantage?

The review discusses the prospects for mitigation-based devices that could deliver a quantum advantage, and lists open problems. This remains a research question and this article makes no claim of deployment.