How do I design a microwave diplexer for multiplexed qubit readout?

A microwave diplexer for multiplexed qubit readout combines or separates readout signals from qubits at different frequencies, enabling multiple qubits to share a single readout line and amplifier chain. In frequency-multiplexed readout, each qubit is coupled to a readout resonator at a unique frequency (typically spaced 50-200 MHz apart within a 4-8 GHz band). The diplexer (or multiplexer for >2 channels) routes specific frequency bands to different qubits or combines signals from multiple resonators onto a single output line. Design considerations: (1) Channel frequencies are set by the readout resonator design, typically fixed on-chip. The multiplexer must match these frequencies with minimal insertion loss (<0.5 dB) in each passband. (2) Isolation between channels (>20 dB) prevents readout tone leakage from one qubit's resonator exciting another qubit. (3) The multiplexer must operate at millikelvin temperatures, requiring superconducting or very-low-loss normal-metal construction. (4) Power handling is not a concern (readout signals are at the single-photon level, <-100 dBm). Common implementations: on-chip multiplexers using coupled CPW resonators fabricated alongside the qubits (most compact, lowest loss), PCB-based multiplexers using microstrip filters on low-loss substrates (more flexible for prototyping), and Purcell filter networks that simultaneously provide frequency multiplexing and qubit protection from T1 decay through the readout port. Current systems multiplex 5-16 qubits per readout line, with research targeting 50+ qubits per line using kinetic-inductance-based multiplexers.