Hardware & Errors
Quantum Error Mitigation
Techniques for reducing the impact of noise on NISQ-era quantum results without full quantum error correction's qubit overhead.
Definition
Quantum error mitigation refers to a family of techniques that reduce the effect of noise on quantum computation results through clever classical post-processing or modified measurement strategies, rather than the much more resource-intensive approach of full quantum error correction using logical qubits.
In depth
Quantum error mitigation is a set of techniques for improving the results of noisy quantum computers without correcting individual errors. Instead of encoding qubits redundantly, mitigation runs extra circuits, often with deliberately modified noise, and combines the results classically so that the estimated expectation value is closer to the noise-free value. It is the main tool for getting useful answers from devices with hundreds of qubits today, and it was used in IBM's 2023 utility experiment on 127 qubits.
The two best-known methods are zero-noise extrapolation and probabilistic error cancellation. Zero-noise extrapolation runs the circuit at several amplified noise levels, for example by stretching pulses, and extrapolates back to zero noise. Probabilistic error cancellation represents ideal gates as a weighted combination of noisy operations that can be run, with some negative weights, and samples from it. Other methods include symmetry verification, which discards results that violate known conservation laws, readout error correction with calibration matrices, and virtual distillation, which uses multiple copies of the state.
The cost is statistical. The number of shots needed grows exponentially with the amount of noise in the circuit, and Quek and coauthors proved in 2022 that this is true for any error mitigation scheme in general. Mitigation therefore works for circuits of moderate size and for estimating expectation values, not for producing full samples of long computations. It is a bridge technology that allows experiments on noisy devices, and it does not replace error correction for long algorithms such as Shor's.
Technical Definition
Common techniques include zero-noise extrapolation (running circuits at deliberately varied noise levels and extrapolating to a zero-noise estimate) and probabilistic error cancellation, both of which trade additional classical computation or repeated runs for improved accuracy without extra physical qubits.
Visual Explanation: An Analogy
Think of error mitigation like noise-canceling techniques in audio recording — rather than building a perfectly silent recording studio (the equivalent of full error correction), you use clever processing to reduce the impact of the noise that's already there.
Key facts
| Item | Detail |
|---|---|
| Zero-noise extrapolation | Amplify noise, measure, and extrapolate to the zero-noise limit |
| Probabilistic error cancellation | Sample from signed combinations of noisy operations; cost grows exponentially with noise |
| Used in | IBM's 2023 127-qubit utility experiment and many variational algorithm demonstrations |
| Fundamental limit | Sampling cost grows exponentially with circuit depth (Quek et al., 2022) |
| Works for | Expectation values, not full output distributions of long circuits |
Where the idea comes from
Temme, Bravyi, and Gambetta and Li and Benjamin introduced the main methods in 2017, and Kandala and colleagues at IBM demonstrated that mitigation extends the reach of a noisy processor in 2019.
Real-World Use Cases
- Already widely used in practice on real NISQ hardware in VQE and QAOA experiments today
- A practical bridge technology until full quantum error correction becomes feasible at scale
How it differs from related ideas
- Error mitigation improves final estimates, while error correction fixes errors during the computation.
- Mitigation needs no extra qubits for most methods, and correction needs many.
- Dynamical decoupling suppresses noise at the pulse level, and mitigation corrects residual effects in post-processing.
Frequently asked questions
What is quantum error mitigation?
Techniques that reduce the effect of noise on measured results by running extra circuits and post-processing, without correcting errors during the computation.
Can mitigation replace error correction?
No. Its cost grows exponentially with circuit size, so it only works for moderate circuits.
What is zero-noise extrapolation?
A method that measures a result at several increased noise levels and extrapolates to the result with no noise.
Related Terms
Keep exploring
- Algorithm: Quantum Error Mitigation Techniques
- Algorithm: Variational Quantum Eigensolver (VQE)
- Algorithm: Quantum Error-Correcting Codes (Shor Code, Surface Code)
- Hardware: IBM Heron (r1, r2, and r3)
- Hardware: IBM Eagle