Error mitigation: zero-noise extrapolation and probabilistic error cancellation
Algorithms and benchmarks / Error mitigation
Techniques that reduce the effect of noise on measured expectation values of short circuits, without the extra qubits of error correction.
- Era
- Noisy intermediate-scale (NISQ)
- Problem class
- Error mitigation
- Speedup
- Not a speedup: it trades more circuit runs for less bias.
How it works
Zero-noise extrapolation runs the circuit at amplified noise levels and extrapolates (Richardson) to zero noise; probabilistic error cancellation resamples randomised circuits according to a quasi-probability distribution to cancel errors (Temme et al. 2017).
Typical use cases
- Every NISQ application that estimates expectation values (VQE, dynamics, kernels).
Resource estimates
No resource estimate with stated assumptions was verified for this family in this release.
Demonstrations
- 2024: Mitigated results of IBM’s 127-qubit kicked Ising experiment were later matched and surpassed by a classical tensor-network simulation. (J. Tindall et al. 2024)
Hardware platforms that fit
Platform-independent: used on all gate-based NISQ devices.
What you need to run it
- Classical simulation
- Noise models can be simulated with density matrices (4^n entries, see the calculator).
- Noisy hardware (NISQ)
- Many more shots than the unmitigated circuit and well-characterised noise (benchmarking results feed the methods).
- Fault-tolerant machine
- Not applicable for this family.
- Annealer or analogue simulator
- Not applicable for this family.
Software
Other open-source frameworks
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- It applies to expectation values, not to individual samples, and it does not replace error correction.
- Mitigation costs extra circuit runs, for example at several amplified noise levels.
In the Quantum Algorithm Zoo
No matching Zoo entry was found on 23 October 2026; the Zoo lists algorithms with a proven or conjectured speedup, not this family.
Index: the Quantum Algorithm Zoo by Stephen P. Jordan, last updated 2026-09-10, checked 2026-10-23. The portal links to it and copies no description from it. Browse the full Quantum Algorithm Zoo (external site)
Named in European procurements
None of the procurement documents read for this release names it.
Sources
- K. Temme, S. Bravyi, J. M. Gambetta (2017). Error mitigation for short-depth quantum circuits. Phys. Rev. Lett. 119, 180509 (2017); arXiv:1612.02058. Read: abstract page, retrieved 2026-10-23.
- J. Tindall, M. Fishman, M. Stoudenmire, D. Sels (2024). Efficient tensor network simulation of IBM's Eagle kicked Ising experiment. PRX Quantum 5, 010308 (2024); arXiv:2306.14887. Read: abstract page, retrieved 2026-10-23.