Accuracy, fidelity and noise

Accuracy says whether the answer is as good as the classical baseline's. Fidelity says how closely the quantum output matches a perfect, noise-free machine. They measure different things, so a run on real hardware can have a correct answer and a low fidelity at once.

Accuracy

Accuracy compares the quantum method's result with the baseline's on the same input. 100% means they are equal. Each workflow declares which of three definitions applies and states it in a note on its page.

A result matches the baseline when any one of these holds: the values are equal; the difference is within a tolerance the workflow declared (molecular-ground-state and interaction-energy declare 1.6 mHa, chemical accuracy); or the difference is statistically indistinguishable from zero given the result's error bar. The verdict reads either "Matches the best classical answer" or "Below the best classical answer".

Chemistry accuracy figures look very high because total energies are large numbers: an error of a few millihartree is a few thousandths of a percent. Read the error in mHa and compare it with 1.6.

Fidelity

Fidelity runs from 0% to 100% and says how close the measured output distribution is to the ideal one. Qsolve computes the raw fidelity itself. It simulates each circuit noise-free (up to 20 qubits) and compares the ideal distribution with the counts that came back, weighted by shots and covering only the circuits that compute something, not calibration or mirror circuits. If some circuits are too large to score, the share of shots that could be scored is recorded as coverage.

Two companion figures sit beside it:

• Fidelity floor. Even a perfect machine only samples, so its measured fidelity is a little under 100%. The floor is the best score possible at your shot count. A result at the floor is as good as it can be.
• Shots kept. The share of shots that passed the workflow's validity checks. Discarding invalid shots is called post-selection. For a portfolio problem that must pick exactly 4 assets, a shot with 5 assets selected is invalid.

A workflow usually applies error mitigation to the counts: readout correction, post-selection and, in the chemistry workflows, zero-noise extrapolation. The mitigation steps are the workflow's own. Qsolve recomputes the resulting fidelity against the ideal output, but the run page still labels it "Fidelity after mitigation (reported)" and shows the raw figure beside it.

Why a correct answer can come with a noisy distribution

The QAOA workflows (generic-qubo, max-cut, portfolio-optimization) measure a circuit many times and take the best outcome among the samples. An ideal circuit puts most of its probability on good solutions. A noisy chip spreads probability onto wrong outcomes too. The whole distribution ends up far from the ideal one, so fidelity is low, yet the best outcome that appeared can still be optimal, and accuracy against the baseline is 100%.

In an illustrative case, if the correct answer has 40% probability on a perfect machine and 3% on a noisy one, fidelity drops a lot, but with 4,000 shots it still appears about 120 times and is still the one returned.

Chemistry is the opposite. VQE reads the energy as an average over the whole distribution, so noise moves the energy directly. Error mitigation does most of the work there, and the step-by-step table on the run page shows what each step recovers. Chemistry results on hardware can miss chemical accuracy even after mitigation.

For sampling workflows, accuracy is the number that matters and fidelity tells you how fragile it was. For averaging workflows both matter, and fidelity predicts the error.

Where the noise came from

Every fidelity figure is labelled with the kind of machine behind it:

Only simulator results count towards a workflow's headline accuracy. Hardware results get their own table, because on today's devices they measure the device as much as the workflow.

Measured or reported

Qsolve computes accuracy, the match verdict, the error bar, qubits, depth, two-qubit gates, circuits, shots and raw fidelity itself. It re-scores each method's solution with the workflow's scoring function, and where a method returns no solution to re-score (a measured energy, say) the value is labelled "Reported by the workflow". Mitigated fidelity, shots kept and mitigation steps are reported by the workflow, and Qsolve recomputes the fidelity.

The workflow supplies the text that describes each method and how accuracy is defined. It does not write the numbers. As a further check, Qsolve compares the shots and circuits it metered with those the result accounts for, and a mismatch stops the run as an integrity failure.