Randomized Benchmarking
Randomized benchmarking estimates average gate error from how quickly random gate sequences decay, cleanly separating gate error from readout error.
The idea
Directly measuring one gate's error is confounded by imperfect state preparation and readout. Randomized benchmarking (RB) sidesteps this. Apply a random sequence of Clifford gates of length m, then a final gate that should return the qubit to its start. Measure the survival probability. Repeat over many random sequences and many lengths.
Why it works
Averaging over random Clifford sequences turns arbitrary gate errors into a simple depolarizing channel, so the survival probability decays exponentially with sequence length: p(m) = A*r^m + B. The decay parameter r gives the average error per Clifford, independent of the constants A and B that absorb state-preparation and measurement errors. That separation is RB's key strength.
Variants
- Standard RB: average error per Clifford gate
- Interleaved RB: insert a specific gate to isolate its error
- Simultaneous RB: run on neighbors at once to reveal crosstalk
- Purity benchmarking: separates coherent from incoherent errors
Strengths and limits
RB is efficient, robust to measurement error, and modality-agnostic, which is why it is the field's standard error metric. Its limits: it reports only an average over the Clifford group, can miss non-Markovian or context-dependent errors, and a single number hides whether errors are coherent (calibratable) or incoherent (fundamental). It also does not directly predict performance on non-Clifford algorithm circuits.
For a fuller picture, teams pair RB with gate-set tomography and application-level benchmarks such as quantum volume, but RB remains the quick, trustworthy gauge of raw gate quality.