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Cycle benchmarking

Component-level

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.

Measures
Composite process fidelity of a cycle of parallel gates under Pauli twirling
Introduced by
Erhard, Wallman & colleagues (Innsbruck & Waterloo) (2019)
Also known as
CB

Cycle benchmarking (CB) measures how well a processor executes a cycle (one clock step of gates applied in parallel across a register) rather than a single gate in isolation. Introduced in 2019 by Erhard, Wallman and colleagues at Innsbruck and Waterloo and demonstrated on a trapped-ion system, it was designed as a scalable alternative to interleaved randomized benchmarking for multiqubit layers, capturing the crosstalk and correlated noise that only appear when everything fires at once.

How it works

The register is prepared in an eigenstate of a chosen n-qubit Pauli operator. The target cycle is then applied m times, each repetition dressed with a layer of random single-qubit Pauli gates; the twirl converts the cycle’s noise into an effective Pauli channel, so the expectation value of the (propagated) Pauli operator decays exponentially in m. Fitting that decay gives a fidelity for one Pauli channel, and averaging the fits over a modest random sample of Pauli operators estimates the composite process fidelity of the whole cycle. Like randomized benchmarking, the estimate is SPAM-robust: preparation and measurement errors shift the decay’s amplitude, not its rate.

Strengths and limitations

CB scores gates in their real operating context (parallel, with neighbors active) and scales: the original experiment benchmarked trapped-ion cycles of 2 to 10 qubits, with process fidelities from 99.6% for two-qubit gates to 86% for a ten-qubit entangling operation, and found error rates consistent as the system grew. The caveats are structural: the standard analysis assumes cycles that map Pauli operators to Pauli operators (Clifford-like cycles), and the score describes the dressed cycle under Pauli twirling: the random Pauli layer is folded in, and coherent errors contribute only through their twirled, stochastic component.

Notable results

CB is commercialized in Keysight’s True-Q suite (originally Quantum Benchmark Inc.), where its per-Pauli decays also feed cycle error reconstruction. A generalized cycle benchmarking extends the idea to cycles containing mid-circuit measurements.

Key papers

Reference implementations

  • Randomized Benchmarking : Estimates average gate error from the exponential decay of survival probability over increasingly long random Clifford sequences, robust to state-preparation and measurement errors.
  • 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.
  • Cycle error reconstruction : Keysight True-Q diagnostic that reconstructs the probabilities of the individual Pauli errors afflicting a cycle of parallel gates, with multiplicative precision