Quantum Error Mitigation Techniques in Noisy Quantum Systems

Noisy quantum hardware presents a fundamental barrier to achieving reliable quantum advantage in the near term. Quantum error mitigation (QEM) encompasses a suite of strategies that reduce the impact of errors without the full overhead of fault‐tolerant quantum error correction. These methods operate at the level of expectation values or quantum states, employing techniques such as zero‐noise extrapolation, probabilistic error cancellation and virtual distillation to infer ideal observables from noisy data. Alternative approaches include subspace expansions and symmetry verification, which exploit inherent structures or conserved quantities in quantum circuits. Recent advances also harness classical post‐processing, machine‐learning optimisation and importance sampling to tailor mitigation to specific noise profiles. By combining experimental calibration, theoretical modelling and efficient classical computation, QEM has enabled practical demonstrations on up to hundreds of qubits, laying the groundwork for applications in chemistry, optimisation and machine learning even before fault tolerance is realised.

Research from Nature Portfolio

A landmark experiment on a 127‐qubit superconducting processor demonstrated accurate measurements of complex circuit expectation values beyond the reach of classical simulation. Improved coherence, fine‐tuned calibration and comprehensive noise characterisation enabled the extraction of correct outputs where leading tensor‐network approximations failed, illustrating the power of tailored error mitigation in the pre‐fault‐tolerant era. In parallel, a post‐processing decoder based on subspace expansions has been developed for logical qubits encoded in small quantum codes. By applying existing code stabilisers without additional syndrome measurements or feed-forward, this method achieves a pseudo-threshold close to 50 % under depolarising noise, and has been validated on both prototype devices and simple molecular simulations.

Research from all publishers

Classical shadows, a technique for predicting many properties of quantum states from few measurements, have been extended with probabilistic error cancellation to produce unbiased estimators of noise-free states. This framework maintains the sample complexity of conventional shadows up to a known overhead that depends on gate noise, enabling efficient characterisation of large‐scale devices. Studies of error statistics reveal that, after mitigation, the intrinsic error scales sublinearly with circuit size—approximately as the square root of gate count—suggesting enhanced suppression in deeper circuits and motivating importance Clifford sampling for scalability. Meanwhile, learning-based protocols employ classically simulatable variants of quantum circuits to train optimal compensation strategies for unknown or correlated noise. These adaptive schemes have demonstrated significant error reduction on real hardware, automatically tuning mitigation to the prevailing noise landscape without exhaustive prior modelling.

Quantum Error Mitigation Techniques in Noisy Quantum Systems publication trend

The graph below shows the total number of articles in quantum error mitigation techniques in noisy quantum systems across all publications each year (not limited to Nature Index journals).

Technical terms

Noisy Intermediate-Scale Quantum (NISQ): A regime of quantum processors with tens to hundreds of qubits subject to significant gate and measurement errors.

Zero-Noise Extrapolation (ZNE): A technique that deliberately varies noise levels in repeated experiments and extrapolates measurements to the zero-noise limit.

Probabilistic Error Cancellation (PEC): A method that represents noisy operations as a weighted combination of ideal and error channels, enabling unbiased estimation at the cost of increased sampling.

Classical Shadows: An approach to estimate multiple state properties from randomised measurements, now augmented with error-mitigation corrections.

Subspace Expansion: A post-processing strategy that projects noisy states into a subspace spanned by known stabiliser operators to suppress errors.

Virtual Distillation: An error-suppression scheme that entangles and measures multiple copies of a noisy state to approximate a purified target without explicit purification circuits.

References

1. Evidence for the utility of quantum computing before fault tolerance. Nature (2023).
2. Quantum Error Mitigated Classical Shadows. PRX Quantum (2024).
3. Error statistics and scalability of quantum error mitigation formulas. npj Quantum Information (2023).
4. Learning-Based Quantum Error Mitigation. PRX Quantum (2021).
5. Virtual Distillation for Quantum Error Mitigation. Physical Review X (2021).
6. Decoding quantum errors with subspace expansions. Nature Communications (2020).