# Techniques: Randomized Benchmarking with Stabilizer Verification and Gate Synthesis

## What the paper contributes (one paragraph)
The paper presents two modifications to Clifford randomized benchmarking (RB) tailored to NISQ hardware. First, it removes the inverse-gate step (and its unrealistic noise assumptions) from Clifford RB by importing the Stabilizer Verification protocol of Markham and Krause: many repetitions of a single random Clifford sequence are checked with local Pauli stabilizer measurements, yielding a benchmarking scheme the authors call RBSV. RBSV produces the usual average-error figure of merit and adds a second one, the verification acceptance probability, which lower bounds the sequence fidelity and serves as a go/no-go failure signature. Second, the paper combines gate synthesis with interleaved RB so that the fixed Clifford element is built from single-qubit Cliffords plus a small number of non-Clifford native gates placed in cancelling positions, enabling characterisation of the average error per non-Clifford gate. Both techniques are accurate only in low-error regimes and are validated numerically on a two-qubit depolarising model.

## Techniques offered
- **Randomized benchmarking with stabilizer verification (RBSV)** - an inverse-free Clifford RB scheme that benchmarks a gate-set by checking repeated random sequences with local Pauli stabilizer measurements, supplying an average gate error and an acceptance-probability figure of merit.
  - guarantee: statistical bound, the extracted parameter upper bounds the true average gate-set error ($r_{rbsv} \geq r$) and the acceptance probability lower bounds the sequence fidelity, acting as a failure signature.
  - quote: "we call our method Randomized Benchmarking with Stabilizer Verification (RBSV)."
- **Interleaved RB with gate synthesis (iRB+GS)** - a modification of interleaved RB in which the fixed Clifford element is synthesised from Clifford and non-Clifford native gates so that the average error per non-Clifford gate can be characterised.
  - guarantee: statistical bound, the estimate $r_N^{est}$ of the non-Clifford gate infidelity is bounded against the true average error for depolarising, delta-depolarising, and Pauli noise channels.
  - quote: "With this simple modification, iRB+GS provides a way to benchmark any non-Clifford or native gate that can compose with other Clifford gates such that the overall element is Clifford."

## Where it could apply
- Target primitive(s): native/generator gate-set characterisation, Clifford and non-Clifford gate benchmarking (applicable to the gate layers underlying VQE, QAOA, and other NISQ circuits).
- Target application group(s): platforms_tooling, error_correction.

## Caveats
Both techniques are reliable only in low-error (high-fidelity) regimes: RBSV requires the verification acceptance probability close to 1 and inherits the low noise-robustness and soundness limits of stabilizer verification, so it cannot characterise systems with substantial or complex noise. iRB+GS relies on assumed near-noiseless single-qubit gates, an identical and composing noise channel per non-Clifford gate, and a hand-built (brute-force) synthesis rather than a systematic recipe. Numerical validation is limited to a two-qubit depolarising model without SPAM errors.