DRAPE — simultaneous calibration of rotation and phase errors in a single experiment

Code, data and figures for

Tien D. Nguyen and Hung Q. Nguyen, Simultaneous calibration of rotation and phase errors in a single experiment, arXiv:2607.19187 (2026).

A symmetric π/2 pulse on a weakly anharmonic qubit realises the gate 𝒳(π/2) = Z(δ) X(π/2 + ε) Z(δ), where the over/under-rotation ε is set by the pulse area alone and the phase error δ depends on ε. DRAPE (DRAG + amplified phase error) is the Ramsey-type sequence Y(π/2) [X(−π/2) X(π/2)]^k X(π/2) read at the fixed axis φ = π/2 while the DRAG coefficient β is swept: the k curves cross at β₀ (the phase correction, estimated with Heisenberg scaling in k) at the height cos²ε/2 (the rotation error, at the standard quantum limit). The experiment is on the |1⟩↔|2⟩ transition of qubit 109 of ibm_brisbane with 20 ns Gaussian pulses.

Layout

path	what
drape_lib.py	the model: four-level transmon Hamiltonian, Gaussian/DRAG pulses, pulse-level QuTiP simulations of DRAPE and of the rotation-error (ARE/AAE) sequence, and the three equivalent gate-level descriptions of DRAPE (unitary, explicit matrix, closed form in Chebyshev polynomials — Eq. 9 of the paper)
drape_estimator.py	the estimator: locate the crossing, calibrate χ (the β→δ slope, Eq. 10), fit (ε, β₀) with χ frozen, window→0 extrapolation; entry points run_on_npz, scan_window
fisher_information.py	per-shot Fisher information F_εε and F_δδ of the DRAPE circuit (Fig. 1b)
utility.py	IQ-discriminator helpers used by notebook 02b
notebooks/	the analysis, in order (below)
data/measured/	every measurement used, as plain .npz (index in data/measured/README.json)
data/simulated/	pulse-level simulations of the DRAPE and ARE sequences (see below)
figures/	the figure panels of the paper as exported by notebook 09

Notebooks

#	notebook	what it does	runtime
01	01_pulse_demo	builds one DRAG-corrected truncated Gaussian pulse and plots Ω_x, Ω_y	seconds
02	02_extract_lambdas	fits the drive strengths λ₀, λ₁, λ₂ = 0.526, 0.621, 0.753 of the 0–1, 1–2 and 2–3 transitions by overlaying QuTiP Rabi simulations on the measured Rabi oscillations	minutes
02b	02b_rabi12_discriminator	the 1–2 Rabi oscillation of the corrected pulse (job cyb4se57…) and the post-selected IQ clusters of	1⟩ and
03	03_drape_analytic_models	checks that the unitary, explicit-matrix, closed-form and linearised DRAPE models agree	seconds
04	04_drape_pulse_simulation	the pulse-level simulation of the DRAPE β-sweep (drape_lib.simulateDRAPE) with the detuning γ calibrated on the measured sweep, and the noise injection at the measured noise level	hours for the full sweep; the cached results are in data/simulated/
05	05_parameter_extraction	linear-stage then full closed-form fits of (ε, χ, β₀) to a simulated sweep; writes data/simulated/drape_fit_params.npz	minutes
06	06_drape_estimator	the estimator of the paper step by step, with 1σ errors and the window→0 extrapolation (ε = 0.0174 rad = 0.997°, β₀ = −0.3894)	~10 min (Monte-Carlo)
07	07_chi	numerical χ = (λ_j/Δ₂) ∫ Ω̇_x cos θ dt for the 20 ns pulse (−4.98·10⁻², theory) vs the fitted −5.03·10⁻²	seconds
08	08_aae_validation	the ARE/AAE sequence simulated with the bare, ε-corrected, β₀-corrected and fully corrected pulse (drape_lib.simulateAAE)	~15 min
09	09_paper_figures	every panel of the paper's figures (figures/*.pdf)	minutes

Run them from the repository root or from notebooks/ (each notebook moves to the root in its first cell). Outputs are kept in the notebooks, so the numbers can be read without running anything.

Which data is measured and which is simulated

The paper combines measurements on ibm_brisbane q109 (taken between Oct 2024 and Feb 2025 through Qiskit Pulse, which has since been retired from the IBM platform) with pulse-level simulations whose only free parameter, the drift detuning γ = −3.57·10⁻⁴ (relative to Δ₂), was fitted to the measured DRAPE sweep (drape_results_fit_various_gamma.npz is that scan). To make the provenance of every curve explicit:

• measured (data/measured/): the three Rabi oscillations behind λ₀, λ₁, λ₂; the APE fringes of Fig. 2(c) (bare vs DRAG, k = 1, 3, 5, 7); the ARE runs with the bare 0.2512 pulse, with DRAG-Y only, with the rescaled amplitude 0.2365 without DRAG, and with amplitude 0.2365 + DRAG (three repeats); and the DRAPE sweep drape_50pts_-1.0_-0.2_0.2365_asterisk.npz (k = 1, 3, …, 11, 50 β values, amplitude 0.2365), which fixes γ and the empirical noise level (EMPIRICAL_STD in notebooks 04 and 09). Every job id is listed in data/measured/README.json; the raw single-shot IQ data of every job are in the PulsatingPulseShop repository (release v1.0-data).
• simulated (data/simulated/): drape/<amplitude>/drape_sim_*.npz are simulateDRAPE sweeps at the uncorrected amplitude 0.2390 or 0.2512 (and 0.2300 for under-rotation), with 500 β values and k = 1…11 or 1…21; drape_pops = y_fit (the clean simulation) + Gaussian noise at the measured noise level, y_fit is the clean simulation. aae_21pts_0_40_0.2390_0.2363.npz is simulateAAE with the bare (0.2390) and the DRAPE-corrected (0.2364) pulse. The DRAPE sweep of Fig. 1(c) and the ARE panel of Fig. 2(d) are drawn from these files (09_paper_figures.ipynb), and the estimates ε̂ = 0.997° ± 0.395°, β̂₀ = −0.3894 ± 0.0002 are the estimator's output on drape/0.2390/drape_sim_500pts_-0.4_-0.37_0.2390_k1to21.npz and …_-2.0_1.25_0.2390_k1to11.npz (notebook 06).

Reproducing the numbers of the paper

quantity	paper	where
λ₀, λ₁, λ₂	0.526, 0.621, 0.753	notebook 02 → data/measured/lambda_values.npz
χ (theory / empirical)	−4.99·10⁻² / −5.03·10⁻²	notebook 07; drape_estimator.calibrate_chi in notebook 06 (the sign depends on the convention δ = χ(β₀ − β) used in the code)
ε̂, β̂₀	0.997° ± 0.395°, −0.3894 ± 0.0002	notebook 06, Sections 3, 5 and 8
Fisher information, Fig. 1(b)	F_δδ → 4N(k+1)², F_εε → 4Nε²	fisher_information.py, notebook 09
APE δ before/after	2.521° → 0.0052°	notebook 09, Fig. 2(c) cell, from data/measured/ape_data.npz
ARE ε before/after	0.997° → −0.007°	notebooks 08 and 09, Fig. 2(d)

Installation

pip install -r requirements.txt      # numpy, scipy, matplotlib, qutip, scikit-learn, jupyter
jupyter lab notebooks/

Python ≥ 3.10; QuTiP 5 (the simulations use qutip.sesolve with time-dependent coefficients). No Qiskit is needed — the hardware runs are not reproducible on the IBM platform any more, and only their results are used here.

Citation

@article{nguyen2026drape,
  title   = {Simultaneous calibration of rotation and phase errors in a single experiment},
  author  = {Nguyen, Tien D. and Nguyen, Hung Q.},
  journal = {arXiv preprint arXiv:2607.19187},
  year    = {2026}
}

License

MIT — see LICENSE. Tien D. Nguyen, 2026.