Skip to main content
Sandbox Physics

Q019 · Coherent drive / calibration

Rabi Pulse Calibration

Set drive amplitude, phase and detuning, then acquire a duration scan. Infer the actual drive from finite counts and test a calibrated pulse. An amplitude error exposes the difference between a nominal setting and an acquired calibration.

Interactive modelRabi Pulse Calibration
Model positive probability—\text{—}
Positive / negative / rejected—\text{—}
Current-setting trials—\text{—}
Acquired positive fraction—\text{—}
95% Wilson interval—\text{—}
Output-state purity—\text{—}
Actual drive · model truth—\text{—}

SIMULATED ACQUISITION

Make a prediction. Collect the evidence.

No acquired record yet.

Inference from acquired counts

Acquire a scan to estimate the signal.

—\text{—}
Density matrix and count conventions
ρ=I+r⋅σ2\rho=\frac{I+\boldsymbol r\cdot\boldsymbol\sigma}{2}

Latest raw events · full record in CSV
EventSettingOutcome

Scientific basis: Feynman III.6 · MIT 8.05 · NIST Ramsey

Physics tutorial

Calibrate a pulse from counts

BackgroundA coherent square pulse rotates a two-level state around an effective axis. Detuning tilts this axis.

Why it mattersNominal amplitude is insufficient when control electronics introduce calibration error. Duration scans provide a measured population calibration.

Start with the essentials

Focus question
Can the first oscillation maximum always flip the state completely?
One-sentence intuition
Detuning reduces the maximum population. A faster oscillation can coexist with a worse flip.

Core mathematical model

Rotating-frame square pulse; angular frequencies

Hrot=ℏ2(Ωcos⁡φ σx+Ωsin⁡φ σy+Δσz)H_{\rm rot}=\frac{\hbar}{2}(\Omega\cos\varphi\,\sigma_x+\Omega\sin\varphi\,\sigma_y+\Delta\sigma_z)

Rotating-frame square pulse; angular frequencies

Exact two-level population within the rotating-wave model

Pe(τ)=Ω2Ω2+Δ2sin⁡2(Ω2+Δ2 τ2)P_e(\tau)=\frac{\Omega^2}{\Omega^2+\Delta^2}\sin^2\left(\frac{\sqrt{\Omega^2+\Delta^2}\,\tau}{2}\right)

Exact two-level population within the rotating-wave model

Resonant flip and half-flip durations

τπ=12fR,τπ/2=14fR(Δ=0)\tau_\pi=\frac{1}{2f_R},\quad\tau_{\pi/2}=\frac{1}{4f_R}\quad(\Delta=0)

Resonant flip and half-flip durations

Common difficulties

Population is not gate fidelity

Typical misconceptionHigh excited population establishes a faithful quantum gate for every input.

Better mental modelThis experiment tests one initial state and one readout. Process fidelity requires further input states and phase-sensitive measurements.

Fitting assumes a model

Typical misconceptionA drive estimate remains valid without known detuning or inside a real multilevel atom.

Better mental modelThe fit is conditional on known detuning, the stated scan range and an isolated two-level rotating-wave model. Leakage and other levels are excluded.

Run the experiment

  1. 01

    Find the first peak

    Choose Full flip and acquire a duration scan. Read the inferred drive, then set duration to the fitted peak.

    What to observe: The estimate uses binomial likelihood of acquired counts and the independently known detuning.
  2. 02

    Prepare a half flip

    Choose Half flip and compare the end-state Bloch vector and acquired population.

    What to observe: Equal populations are a coherent transverse state, not an unpolarized mixture.
  3. 03

    Expose a calibration error

    Choose Calibration error and acquire a scan. Compare fitted drive with nominal drive.

    What to observe: A 20% amplitude error shifts the optimal time. The display shows settings and inference separately.
  4. 04

    Tilt the rotation axis

    Choose Off resonance, scan and rotate drive phase.

    What to observe: The first peak stays below unity. Phase changes the transverse state while excited population from the ground state is phase independent.