Short answer
There isn’t a single, meaningful “qubit fidelity” number for a D‑Wave annealer, and randomized benchmarking (a gate‑model tool) does not apply. D‑Wave devices are analog quantum annealers; the relevant question is how faithfully the hardware realizes the programmed Ising Hamiltonian over the whole chip. That faithfulness is characterized by control errors and noise rather than gate fidelities, and D‑Wave does not publish per‑qubit calibration/fidelity tables. They do, however, routinely calibrate every qubit and coupler internally and expose mitigation tools (e.g., spin‑reversal transforms, anneal offsets) and some aggregate properties via the API. If you need device‑specific error numbers, you typically have to obtain them directly from D‑Wave (often under NDA) or estimate them yourself with small in‑situ experiments.
What “fidelity” means on a D‑Wave annealer
For an annealer, the natural figure of merit is how closely the implemented time‑dependent Hamiltonian, Hphys(s), matches the intended Ising Hamiltonian, Hprog = Σi hi σz(i) + Σij Jij σz(i)σz(j), and how much thermal and dynamical noise perturbs the evolution. The dominant error sources are:
- Intrinsic control error (ICE): static mis‑specification of programmed local fields hi and couplings Jij (transfer‑function errors, offsets, and drift), and residual crosstalk between control lines.
- Dynamic noise and thermal effects: flux noise, decoherence during the anneal, and thermal excitations near the “freeze‑out” point.
- Readout error: misclassification when measuring the final spin state (typically small compared to ICE/thermal effects).
- Anneal‑path nonuniformity: qubit‑to‑qubit variations in the A(s), B(s) schedules due to device parameter spread (persistent current, junction variability), partly mitigable with per‑qubit anneal offsets.
Because there are no unitary gates, metrics like single‑/two‑qubit gate fidelity or randomized benchmarking aren’t defined. Instead, people report:
- RMS (or distribution) of hi and Jij specification error (a few percent of full‑scale in older generations; improved in recent generations).
- Effective temperature and scaling factors inferred from fitting output distributions to Boltzmann models.
- Problem‑level success probabilities (ground‑state hit rates) on calibration or “planted‑solution” instances, often with gauge averaging.
What D‑Wave calibrates and exposes
D‑Wave performs extensive, scalable, largely local calibrations using only 1‑ and 2‑qubit experiments (so they scale linearly with qubit/coupler count and are practical even for >5000 qubits). In broad strokes:
- Transfer functions: Map digital control values to physical flux for each qubit (hi) and coupler (Jij), including trimming of offsets and gain.
- Crosstalk compensation: Measure and invert a linear crosstalk matrix so programming one line doesn’t perturb neighbors.
- Anneal‑path equalization: Characterize persistent‑current variations and provide per‑qubit anneal offsets to locally advance/retard the anneal, partially equalizing A(s)/B(s).
- Drift/aging: Periodic recalibration to track slow drift.
- Readout calibration: Optimize SQUID thresholds and timing.
What you can use as a user
- Spin‑reversal (gauge) transforms: Average over spin flips to cancel a large fraction of static biases (ICE).
- Anneal offsets: Per‑qubit schedule shifts to compensate for nonuniformities or to balance chains in embeddings.
- Reverse annealing and anneal‑schedule control: Can help probe local energy landscapes and effective temperatures.
- Device properties via the Ocean SDK: topology, operational qubits/couplers, programmable ranges, and per‑qubit anneal‑offset ranges. Not per‑qubit “fidelities.”
How to estimate “fidelity‑like” quantities yourself
You can measure practical, instance‑relevant error parameters on any accessible D‑Wave system with small experiments:
- Field (hi) transfer/offset: Program all couplers to zero. For each qubit i, sweep hi over its range, collect output magnetization ⟨σz(i)⟩ (with gauges), and fit a tanh curve to extract scale and offset; the offset at hi=0 is the residual bias. Repeat occasionally to see drift.
- Coupler (Jij) transfer/offset: Pair qubits, zero their local fields, sweep Jij, and fit the correlation ⟨σz(i)σz(j)⟩ to extract gain/offset and nonlinearity.
- Effective temperature / freeze‑out: For small instances with known spectra, fit sampled distributions to a Boltzmann model to estimate an effective βeff and any global rescaling of h/J.
- Readout error: Program a strong ferromagnet (all‑up/all‑down), measure fraction of spins flipped after readout; distinguish readout vs thermal by using very short anneals and strong fields.
References and where to look
- D‑Wave documentation site (search for “Intrinsic Control Error (ICE)”, “spin‑reversal transforms”, “anneal offsets”, “QPU properties”): https://docs.dwavesys.com/
- M. W. Johnson et al., “Quantum annealing with manufactured spins,” Nature 473, 194–198 (2011) – device and calibration concepts.
- R. Harris et al., “Experimental investigation of an eight‑qubit unit cell in a superconducting optimization processor,” Phys. Rev. B 82, 024511 (2010) – qubit/coupler characterization.
- Empirical characterizations by external groups often report ICE and effective temperatures; see, e.g., studies by Albash, Lidar, and collaborators on benchmarking/identification of annealers.
Bottom line
- There is no single per‑qubit fidelity metric published by D‑Wave; gate‑model tools like randomized benchmarking don’t apply.
- The relevant figures of merit are control accuracy for hi/Jij (ICE), thermal/noise effects, and readout error; D‑Wave calibrates these internally with scalable 1‑ and 2‑qubit procedures and provides mitigation tools.
- If you need quantitative numbers for a specific system, either contact D‑Wave support for calibration summaries or estimate them in situ with the small experiments outlined above and use gauge averaging and anneal offsets to mitigate residuals.