SlotLayer 0
Recover a noiseless expectation value by post-processing
Estimate what an observable would have measured on a noiseless device by running modified or repeated circuits on the noisy one and combining the results classically. No qubits are spent on redundancy; the whole price is paid in shots.
A circuit, a target observable, a noisy device, a shot budget, and — for the model-based methods — a learned characterization of the device noise.
A bias-reduced expectation-value estimate, with a variance — equivalently a sampling overhead — that grows with circuit volume.
This one, drawn
From Noisy expectation value to Bias-reduced expectation value
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Why this is a layer
Mitigation and correction are different contracts, not different degrees of the same one. Correction returns logical qubits a later subroutine can consume coherently; mitigation returns a statistic, and nothing downstream can take its output as a quantum input, so an algorithm whose result is a sampled bitstring cannot use it at all. It is also the one layer here with a proven ceiling: the sampling overhead of any protocol in a broad class — including protocols with nonlinear post-processing and protocols not yet invented — grows exponentially with circuit depth for layered circuits under local depolarizing and, more broadly, Markovian noise, and for random circuits under local noise with qubit count as well. Those are worst-case, class-wide bounds, so particular structured instances can still be mitigated cheaply — which is why mitigation remains a useful small-scale instrument and not a scaling path.
Ways to do this
4 methods recorded
- Zero-noise extrapolation (ZNE)
Deliberately amplify the device noise by a set of known factors, measure the observable at each, and extrapolate the resulting curve back to zero noise. The fit is Richardson's deferred approach to the limit, or another model.
- Probabilistic error cancellation (PEC)
Write the inverse of the characterized noise channel as a quasi-probability distribution over implementable operations, sample circuits from it, and combine the results with signed weights. Unlike extrapolation it inverts the noise rather than fitting through it, so it is unbiased in principle.
- Readout (measurement) error mitigation
Correct the classical readout channel by deconvolving the assignment matrix that maps true bitstrings to observed ones. The naive form calibrates and inverts the full matrix; the scalable form never forms it.
- Check the symmetries the answer must have
The physics fixes quantities the true state cannot change — particle number, spin. Measure them alongside the run and discard, or post-process away, the outcomes that violate them: an error that moves the state out of the sector announces itself, and one that keeps it inside does not.
Routes that skip this layer
No recorded route avoids this step.
This is a step inside
Nothing in this graph needs this as a step, so it is where a reading starts.
In the Atlas
No record in the Atlas covers this yet. The catalogue is circuits and primitives; this part of the literature is not in it.