Randomized Benchmarking

Randomized benchmarking (RB) is the workhorse protocol for characterizing gate error rates. Vendors’ quoted single- and two-qubit fidelities are, more often than not, RB numbers. Its key virtue is separating gate error from state-preparation and measurement (SPAM) error, which plagues naive fidelity estimates.

How it works

The standard protocol samples random sequences of m Clifford gates, appends the single Clifford that inverts the whole sequence, and measures the probability of returning to the initial state. Averaged over many random sequences, this survival probability decays exponentially, as A·p^m + B, where the constants A and B absorb SPAM errors. The decay parameter p yields the average error per Clifford, r = (d − 1)(1 − p)/d with d = 2^n.

Clifford gates are used because they form a unitary 2-design — averaging over them twirls arbitrary noise into an effective depolarizing channel, which is what makes the simple exponential model valid — and because Clifford circuits are efficiently classically simulable, so the inversion gate is cheap to compute.

Variants

A large family of protocols extends the idea: interleaved RB inserts a specific gate between random Cliffords to estimate that gate’s individual error; simultaneous RB runs RB on neighboring qubits concurrently to expose crosstalk; direct RB, mirror RB, and cycle benchmarking scale the approach to wider circuits and native (non-Clifford) gate sets. See Helsen et al.’s framework paper for a unified treatment.

Strengths and limitations

RB is efficient (polynomial in qubit number), SPAM-robust, and standardized enough that numbers are roughly comparable across labs. Its limitations: it reports an average error over the Clifford group, not worst-case behavior; compiling multi-qubit Cliffords into native gates is costly, so plain Clifford RB is mostly practical at one or two qubits; and strongly gate-dependent noise can bias the extracted rate, which is why interpretation subtleties remain an active research topic.