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Deterministic Benchmarking

Component-level proposal

Deterministic single-qubit protocol that separates coherent from incoherent gate errors with a handful of fixed two-pulse sequences instead of the random circuits of RB.

Measures
Four parameters splitting a single-qubit gate set's coherent (calibration/control) and incoherent (decoherence) errors, fit from fidelity decays of fixed pulse-pair sequences
Introduced by
Tripathi, Levenson-Falk, Lidar & colleagues (USC) (2024)
Also known as
DB

Deterministic benchmarking (DB) is a single-qubit gate-set benchmark proposed in 2024 by Tripathi, Kowsari, Saurav, Zhang, Levenson-Falk and Lidar at the University of Southern California. It is positioned as a cheaper, deterministic alternative to randomized benchmarking: instead of averaging over many random gate sequences, it runs a small fixed set of two-pulse sequences and separates the gate set’s coherent (calibration and control) errors from its incoherent (decoherence) errors.

How it works

DB tracks state fidelity under repeated two-pulse blocks built from the gate set under test, dynamical-decoupling-style sequences of increasing length. Fitting the decay curves to the authors’ analytical model yields four error parameters that jointly characterize the coherent and incoherent error channels of the single-qubit gate set, including coherent errors that a conventional RB decay can miss. Because the sequences are fixed rather than sampled, the protocol needs far fewer experimental runs than RB while remaining resilient to state-preparation and measurement (SPAM) errors. The authors demonstrated it on a USC superconducting transmon, with master-equation simulations backing the analytical model.

Strengths and limitations

DB’s appeal is diagnostic information per shot: one inexpensive experiment splits an error budget that a single RB number conflates, placing it between RB and full characterization methods like gate set tomography. Its output is a four-parameter decomposition rather than one scalar score: like unitarity RB, it distinguishes coherent from incoherent noise, but deterministically.

So far it is defined and demonstrated only for single-qubit gate sets; the two-qubit extension is explicitly future work, and no public reference implementation exists. One citation trap: v1 of arXiv:2407.09942 (July 2024) is the protocol paper “Deterministic Benchmarking of Quantum Gates”, but v2 became the broader Chemical Reviews survey “Benchmarking quantum gates and circuits”; DB is the novel protocol inside that review, so citations of the review are not necessarily uses of DB.

Notable results

As of July 2026 DB remains a proposal: demonstrated by its authors on one superconducting qubit, published within the review at Chem. Rev. 125, 5745 (2025), and disseminated through seminars and press coverage, but with no independent third-party deployments reported.

Key papers

  • 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.
  • 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.
  • 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.