Coherent vs Incoherent Gate Errors
Not all gate errors accumulate the same way with circuit depth — the distinction matters for predicting how badly a deep circuit will actually degrade.
- Coherent (systematic) errors — deterministic miscalibration, e.g. a gate that over-rotates by a small fixed angle every time. In principle correctable if you knew the exact miscalibration.
- Incoherent errors — decoherence-driven, fundamentally stochastic (see Physical Decoherence Mechanisms). Not correctable by better calibration, because there’s no fixed error to calibrate away.
- Crosstalk — a third category, from unwanted coupling between qubits rather than either qubit’s own imperfection.
Why the distinction matters: different depth scaling
Key insight: in the short-time/shallow-circuit limit, coherent error accumulates quadratically with circuit depth (small systematic rotations compound coherently, adding up like amplitudes), while incoherent error accumulates linearly (independent random events just add in probability). SPAM errors (state preparation and measurement) add a depth-independent constant offset — they happen once per circuit, not once per layer.
This means two circuits with the same total error budget can behave very differently: a circuit dominated by coherent error gets disproportionately worse as it gets deeper, while one dominated by incoherent error degrades more predictably. Pauli twirling exists specifically to convert coherent error into incoherent (Pauli) error — trading the bad quadratic scaling for the more benign linear one, at the cost of extra randomization overhead.
Related
- Physical Decoherence Mechanisms
- Pauli Error Model
- EstimatorOptions and the Five Mitigation Knobs — Pauli twirling as coherent-to-incoherent conversion
- Readout as a Confusion Matrix
Self-Check
- Could you explain the difference between coherent and incoherent errors, and why only one is “correctable by calibration”?
- Why does coherent error scale quadratically with depth while incoherent error scales linearly?
- Why does Pauli twirling deliberately convert coherent error into incoherent error, given incoherent sounds worse?