What is the required channel-to-channel isolation in a multi-qubit control electronics system?

The required channel-to-channel isolation in a multi-qubit control electronics system prevents the control signal for one qubit from inadvertently affecting adjacent qubits, which would cause crosstalk errors. The isolation requirement depends on the qubit's sensitivity to off-resonant drive signals and the target gate error rate. For a transmon qubit: the off-resonant drive error probability scales as (Omega_crosstalk/Delta_f)^2, where Omega_crosstalk is the Rabi rate from the crosstalk signal and Delta_f is the frequency detuning between the target qubit and the crosstalk qubit. For a target error rate of 10^-4 (0.01%) and Delta_f = 100 MHz: Omega_crosstalk must be less than approximately 1 kHz. If the intended qubit drive Rabi rate is Omega_target = 10 MHz (corresponding to a 25 ns gate): the required isolation = 20log10(Omega_target/Omega_crosstalk) = 20log10(10e6/1e3) = 80 dB. In practice: 60-80 dB of channel-to-channel isolation is required in the control electronics, depending on the qubit frequency separation and the desired gate fidelity. Sources of crosstalk: direct electrical coupling between DAC channels (PCB trace coupling, shared power supply, ground loops), mixer LO leakage and sideband products (spurs from the upconversion process that fall on adjacent qubit frequencies), and cable-to-cable coupling inside the cryostat (adjacent microwave cables coupling through shared connectors or insufficient shielding).