Zero Noise Extrapolation Error Mitigation

Short answer: Zero-noise extrapolation (ZNE) is an error mitigation technique: run a circuit at several deliberately increased noise levels, then extrapolate the results back to what a noise-free run would give. Probabilistic error cancellation (PEC) is another post-processing method. A 2023 Reviews of Modern Physics review describes mitigation as the route for noisy machines before fault tolerance, and IBM's documentation notes ZNE often improves results but does not always give an unbiased answer. Mitigation reduces error in estimated averages. It does not correct the computation itself.

Why mitigate instead of correct

A 2023 Reviews of Modern Physics review says that in the era of noisy intermediate-scale quantum machines one must seek to mitigate errors rather than eliminate them completely, since quantum fault tolerance is the answer only in the long term. It surveys the methods proposed, assesses their in-principle efficacy and describes hardware demonstrations to date. It identifies commonalities and limitations, says methods can be chosen according to the primary type of noise present, and discusses the prospects for mitigation-based devices that could deliver a quantum advantage. The review lists open problems, so this remains an active research area.

How ZNE works

IBM's documentation describes ZNE as a technique for mitigating errors in estimating expectation values of observables. It has two stages. First is noise amplification, where the original circuit is executed multiple times at different noise rates. Second is extrapolation, where the ideal result is estimated by extrapolating the noisy expectation values to the zero-noise limit. The documentation says both stages can be implemented in many ways. It describes one amplification method, digital gate folding, which replaces two-qubit gates with equivalent sequences of the gate and its inverse, so that replacing a unitary U with U, then its inverse, then U gives a noise amplification factor of 3. For the extrapolation it offers functional forms including linear and exponential fits.

The documentation states that while ZNE often improves results, it is not certain to produce an unbiased result. It also says the overhead scales with the number of noise factors, and that the default settings sample three noise factors, giving a roughly threefold overhead. These details describe IBM's implementation of the technique.

A broader survey

A 2026 survey in an ACM journal says quantum noise is a significant challenge for near-term quantum computing and that error mitigation has emerged as a key strategy, particularly for variational quantum circuits. It separates techniques applied during training, such as optimal control and dynamical decoupling, from post-processing techniques, naming zero-noise extrapolation and probabilistic error cancellation. For each technique it covers fundamentals, mitigation concepts and recent advances. It also describes software toolboxes, including Mitiq and Qiskit Aer, and a case study of ZNE guided by a contextual multi-armed bandit. It lists open problems, including machine-learning-assisted mitigation and integration with error correction.

What this does not tell you

These sources do not give the size of the accuracy improvement for any workload. Overhead and bias depend on the circuit, the noise and the choices made in amplification and extrapolation, and the review's open problems include how well mitigation scales.

FAQ

What is zero-noise extrapolation?

Running a circuit at amplified noise levels and extrapolating the results to the zero-noise limit, per IBM's documentation.

How is noise amplified?

One method replaces gates with the gate followed by its inverse and the gate again, which triples the noise.

Is the result always correct?

No. IBM's documentation says ZNE often improves results but is not certain to give an unbiased one.

What is probabilistic error cancellation?

Another post-processing mitigation technique named alongside ZNE in the 2026 survey.

Is this the same as error correction?

No. The 2023 review frames mitigation as a way to cope with noise in the era before fault tolerance.