IQ Mixer Upconversion for Qubit Control

IQ Modulator Errors

Gain imbalance ε 5%

Phase imbalance δφ 3°

LO leakage 2%

Pulse envelope width 45%

Live Readouts

Image rejection

— dB

Carrier leakage

— dBc

Sideband purity (power to intended tone)

—%

Signal Paths

Desired tone f_LO+f_IF → target qubit

Image tone f_LO−f_IF → neighbor qubit (crosstalk risk)

LO leakage at f_LO (always-on bleed)

How it works

A qubit control pulse is synthesized at low (IF) frequency by an arbitrary waveform generator as two channels, I(t) and Q(t), then upconverted to the qubit's microwave frequency by an IQ mixer driven by a local oscillator (LO):

RF(t) = I(t)·cos(ω_LO t) − Q(t)·sin(ω_LO t)
I(t) = A(t)·cos(ω_IF t)
Q(t) = (1+ε)·A(t)·sin(ω_IF t + δφ)   [real hardware's gain/phase error]

With a perfect mixer (ε = 0, δφ = 0) this produces one clean tone at ω_LO + ω_IF — single-sideband upconversion. Any gain imbalance ε or phase imbalance δφ between the I and Q channels lets a second, unwanted tone leak through at the mirror frequency ω_LO − ω_IF (the "image"), with amplitude:

A_upper = ½√(1+(1+ε)² + 2(1+ε)cos δφ)   (desired)
A_image = ½√(1+(1+ε)² − 2(1+ε)cos δφ)   (image)
Image Rejection Ratio = 20·log₁₀(A_upper / A_image)  dB

A real mixer also lets a fraction of the bare LO tone bleed straight through to the output (LO/carrier leakage), independent of any modulation. On a chip crowded with many qubits at different frequencies, the image tone is not just wasted power — if a neighboring qubit happens to sit near f_LO − f_IF, that unwanted tone can off-resonantly drive it, corrupting its state. This is one reason real control electronics are calibrated (DC-offset nulling for LO leakage, gain/phase correction for image rejection) before running any algorithm.

Gain / phase imbalance sliders — set ε and δφ; watch the image-sideband stream grow and the neighbor qubit chip light up.
LO leakage slider — sets the constant carrier bleed glowing at the mixer, independent of the pulse envelope.
Pulse width slider — widens or narrows the Gaussian envelope A(t) that gates every burst.
Presets — "Ideal mixer" zeroes all three error sources; "Typical hardware" loads representative lab-grade calibration residuals.

Target qubit (desired) Neighbor qubit (image crosstalk) LO leakage glow

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