Single-shot readout IQ blob histogram

A two-dimensional histogram of single-shot demodulated readout points, one per measurement, for a qubit prepared equally often in |0> and |1> – the calibration plot that sets the demodulation angle and the discrimination threshold for every single-shot measurement afterward. Each state’s cloud of points is approximately Gaussian, centered where that state’s dispersive response places it in the IQ plane and spread by the same amplifier and thermal noise regardless of which state produced it; the separation between the two clouds relative to their common spread is exactly the SNR that sets assignment fidelity (compare the frequency/duration optimization in Single-shot readout fidelity optimization). Rotating the demodulation phase so the line joining the two blob centers lies along the I axis is what lets a single-quadrature threshold on I alone separate the states, instead of a threshold in the full IQ plane.

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import numpy as np
import polars as pl
import plotpress

N_SHOTS = 60000
SEPARATION = 2.4               # blob center-to-center distance, in noise sigmas
rng = np.random.default_rng(808)

state = rng.integers(0, 2, N_SHOTS)          # 0 or 1, equally likely
angle = 0.35                                   # readout IQ angle, radians
center_g = np.array([0.0, 0.0])
center_e = SEPARATION * np.array([np.cos(angle), np.sin(angle)])

points = np.where(state[:, None] == 0, center_g, center_e)
points = points + rng.normal(0.0, 1.0, points.shape)

# One row per single-shot measurement -- exactly the raw shot table a real
# acquisition would log, before it is ever binned into a histogram.
shots = pl.DataFrame({
    "state": state,
    "i": points[:, 0],
    "q": points[:, 1],
})

counts, i_edges, q_edges = np.histogram2d(
    shots["i"].to_numpy(), shots["q"].to_numpy(), bins=140,
    range=[[-3.5, 5.5], [-3.5, 5.5]])

fig, ax = plotpress.subplots(figsize=(6.6, 5.8))
mesh = ax.pcolormesh(i_edges, q_edges, counts.T, cmap="magma")
bar = fig.colorbar(mesh, ax=ax)
bar.set_title("shots")
ax.set_aspect("equal")
ax.set_xlabel("I (a.u.)")
ax.set_ylabel("Q (a.u.)")
ax.set_title(f"IQ blobs, {SEPARATION:.1f} sigma separation")
fig.tight_layout()