Quantum Benchmark Zoo

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Randomized Benchmarking

Component-level

Estimates average gate error from the exponential decay of survival probability over increasingly long random Clifford sequences, robust to state-preparation and measurement errors.

Measures
Average error per Clifford gate (per-gate error via the interleaved variant), from the decay constant of sequence fidelity
Introduced by
Emerson, Alicki & Życzkowski, Knill et al. (NIST), Magesan, Gambetta & Emerson (2005)
Also known as
RB, Clifford RB

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.

The protocol uses Clifford gates for two reasons: they form a unitary 2-design, so averaging over them twirls arbitrary noise into an effective depolarizing channel and the simple exponential model holds; and Clifford circuits are efficiently classically simulable, so the inversion gate is cheap to compute.

The RB family

RB is a family of protocols, not a single benchmark. Named variants with their own entries in this catalog:

Helsen, Roth, Onorati, Werner & Eisert’s general framework (PRX Quantum 2022) unifies further named variants (filtered, real, dihedral, iterative, and error-specific RB), and Hashim et al.’s tutorial tabulates and compares thirteen of them side by side.

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, so interpretation subtleties remain an active research topic.

Key papers

Reference implementations

  • Interleaved randomized benchmarking : Estimates the error of one specific quantum gate by interleaving it between random Cliffords and comparing the resulting decay against a reference randomized benchmarking curve.
  • Direct randomized benchmarking : Benchmarks random layers of native gates directly instead of compiled multi-qubit Cliffords, measuring gates as they are actually used and scaling well beyond standard RB.
  • Mirror randomized benchmarking : Scalable RB variant built from mirror circuits (motion-reversal sequences with random Pauli layers) that avoids compiling expensive inversion gates and extends layer-error estimates to many-qubit widths.
  • Cycle benchmarking : Pauli-twirled decay protocol that measures the process fidelity of an entire cycle of parallel gates at once, scaling to whole devices where interleaved benchmarking cannot.
  • Unitarity randomized benchmarking : Randomized-benchmarking variant that fits the decay of output-state purity to measure how coherent a gate set's noise is, splitting error budgets into miscalibration and decoherence.
  • Cross-Entropy Benchmarking : Estimates circuit fidelity by checking how often a device samples the high-probability bitstrings of random quantum circuits, the metric behind Google's quantum supremacy claim.
  • Gate set tomography : Calibration-free tomography that reconstructs every gate, state preparation, and measurement in a gate set simultaneously and self-consistently, yielding predictive error models rather than a single score.