DRAG Pulse Shaping — Qubit Leakage Suppression

Drive pulse

Pulse duration 10.0 ns

DRAG correction strength 0.00

Final populations

|0⟩ remaining

–

|1⟩ transferred

–

|2⟩ leakage

–

Optimal λ (this T)

–

How it works

A microwave pulse drives the |0⟩↔|1⟩ transition with a Gaussian envelope Ω_x(t) shaped to deliver a π rotation. A real qubit also has a weakly-detuned |2⟩ level (anharmonicity Δ) that a fast, short pulse can partially populate — that's leakage.

DRAG adds a second quadrature Ω_y(t) = −λ·(dΩ_x/dt)/Δ on the same drive line. This correction destructively interferes with the pathway that excites |2⟩, without changing the intended |0⟩→|1⟩ transfer.

i·dc/dt = H(t)·c
H = [[0, Ω*/2, 0],
     [Ω/2, 0, √2·Ω*/2],
     [0, √2·Ω/2, Δ]]
Ω(t) = Ω_x(t) + i·Ω_y(t)

Pulse duration — shorter pulses need larger Ω_x amplitude to still deliver a full π rotation, which drives |2⟩ harder.
DRAG strength λ — 0 is a plain naive pulse; near 1 the correction is close to the analytic optimum; well past 1 it overcorrects and leakage climbs again.
The lower chart sweeps λ at the current duration and always shows the same characteristic dip at the optimum.

Level populations during the pulset = 0.0 / 10.0 ns

|0⟩ ground |1⟩ target |2⟩ leakage

Final |2⟩ leakage vs DRAG strength λduration fixed at current slider