How do I design a multiplexed readout system that reads multiple qubits through a single amplifier chain?

Designing a multiplexed readout system that reads multiple qubits through a single amplifier chain uses frequency-division multiplexing (FDM) to simultaneously probe multiple qubit readout resonators at different frequencies through a common transmission line and amplifier. Each qubit is coupled to a readout resonator at a unique frequency (typically separated by 20-100 MHz within the 5-9 GHz band). To read all qubits: a multi-tone probe signal is generated containing a tone at each readout resonator's frequency. This combined signal is sent through the common input line to the qubit chip. Each readout resonator responds to only its own probe tone, and the response (phase and amplitude shift) depends on the state of the coupled qubit. All responses travel back through the common output line to a single cryogenic amplifier (HEMT or parametric amplifier), then to the room-temperature receiver. The room-temperature receiver digitizes the wideband signal and demodulates each tone independently (using digital downconversion and filtering) to extract the qubit state from each resonator. The design considerations are: frequency spacing (each readout resonator must be at a unique frequency with sufficient separation to prevent crosstalk; minimum spacing approximately 10-50 MHz depending on the resonator linewidth (typically 1-10 MHz)), amplifier bandwidth (the cryogenic amplifier must have sufficient bandwidth to cover all readout tones; a HEMT amplifier at 4K typically covers 4-8 GHz with less than 5 K noise temperature), and DAC/ADC bandwidth (the room-temperature electronics must generate and digitize a wideband signal spanning all readout frequencies).