How do I design a microwave diplexer for multiplexed qubit readout?
Multiplexed Qubit Readout Design
Frequency multiplexing of qubit readout is the primary strategy for reducing the number of readout cables and amplifiers in large-scale quantum computers. Without multiplexing, each qubit requires its own output line, circulator chain, and amplifier, creating an unsustainable scaling burden.
| Parameter | Option A | Option B | Option C |
|---|---|---|---|
| Performance | High | Medium | Low |
| Cost | High | Low | Medium |
| Complexity | High | Low | Medium |
| Bandwidth | Narrow | Wide | Moderate |
| Typical Use | Lab/military | Consumer | Industrial |
Technical Considerations
Readout resonator frequencies must be spaced to avoid: (1) Direct overlap (obviously). (2) Collision with qubit transition frequencies (readout resonator at 6.0 GHz, qubit at 5.0 GHz, detuning = 1 GHz, dispersive regime requirement: detuning >> coupling g, typically g/2pi = 50-200 MHz). (3) Crossover with other qubits' frequencies via higher harmonics or two-photon transitions. Typical frequency plan for 8 qubits on one readout line: resonator frequencies from 6.0 to 7.4 GHz, spaced 200 MHz apart. Qubit frequencies from 4.5 to 5.5 GHz. The readout probe tones are generated at room temperature and combined into a single cable, pass through the attenuator chain to the chip, interact with each resonator, and the combined response (all 8 frequencies) exits through a single output line to the amplifier. The readout electronics demodulate each frequency to extract individual qubit states.
Performance Analysis
The simplest multiplexer is a common feedline: a single CPW transmission line runs past all readout resonators, which are capacitively coupled to the feedline. Each resonator loads the feedline at its resonance frequency. The feedline acts as a natural frequency multiplexer, combining all resonator signals onto one output. Design parameters: coupling quality factor Q_c = 500-5000 (determines the readout resonator linewidth: kappa = omega_r/Q_c). Lower Q_c gives wider linewidth (faster readout) but more overlap between channels. Higher Q_c gives narrower linewidth (less overlap) but slower readout. For 200 MHz channel spacing and Q_c = 2000 at 6 GHz: linewidth = 3 MHz, giving 200/3 = 67× of frequency separation, sufficient for >30 dB channel isolation. The feedline characteristic impedance and coupling capacitor values must be designed to present the correct Q_c at each resonator while maintaining 50-ohm impedance match across the band.
Design Guidelines
Beyond simple feedline coupling, advanced multiplexing schemes include: (1) Purcell filter networks: bandpass filters between the qubit-resonator system and the feedline that provide protection against qubit energy decay through the readout port (Purcell effect) while allowing readout signals to pass. These filters simultaneously function as channel multiplexers. (2) Kinetic inductance multiplexers: using high kinetic inductance materials (TiN, NbTiN, granular aluminum) to create compact, high-Q resonators with 1-5 MHz spacing, enabling 50-100 resonators per octave of bandwidth. This technique, borrowed from astrophysics detector arrays (MKIDs), is being adapted for qubit readout. (3) Digital multiplexing: using time-division multiplexing (reading qubits sequentially rather than simultaneously) as a supplementary strategy when frequency space is exhausted. The trade-off is increased total readout time proportional to the number of time slots.
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
Implementation Notes
When evaluating design a microwave diplexer for multiplexed qubit readout?, engineers must account for the specific requirements of their target application. The optimal choice depends on the frequency range, power level, environmental conditions, and cost constraints of the overall system design.
Frequently Asked Questions
How many qubits can share one readout line?
Current systems: 5-16 qubits per readout line (Google: 8, IBM: 5-8, Rigetti: 8-16). Practical limits: frequency space (4-8 GHz band divided by 50-200 MHz spacing = 20-80 channels), readout resonator Q (determines minimum spacing without channel overlap), amplifier bandwidth (JPA: ~20 MHz supports 1-3 channels; TWPA: ~4 GHz supports 20-80 channels), and room-temperature electronics (need one DAC/ADC channel per qubit readout frequency). Research demonstrations have shown up to 50+ multiplexed readout resonators in a single band using kinetic inductance detectors, but maintaining qubit readout fidelity with that density has not been fully demonstrated.
What insertion loss is acceptable for the multiplexer?
On the output (readout) side: every dB of multiplexer insertion loss directly degrades readout SNR. Target <0.5 dB. On-chip multiplexers using superconducting CPW resonators achieve insertion loss of 0.1-0.3 dB per channel. PCB-based external multiplexers add 0.5-2 dB due to connector transitions and normal-metal conductor losses. On the input (drive) side: insertion loss is less critical because the signal power can be increased at the source. However, multiplexer loss at the MC stage generates thermal noise at ~20 mK, which is negligible (n_th = 0.083 at 5 GHz), so even 3-5 dB of loss is acceptable if the room-temperature electronics can compensate.
Does multiplexing affect readout fidelity?
Multiplexing can slightly reduce readout fidelity compared to dedicated per-qubit readout through several mechanisms: (1) Residual crosstalk between channels (a strong readout signal from qubit A leaking into qubit B's measurement). With 200 MHz spacing and Q_c = 2000: crosstalk < -30 dB, contributing <0.1% measurement error. (2) Amplifier dynamic range: the TWPA/JPA must simultaneously amplify N readout signals. The total power (N × per-channel power) must remain below the amplifier P1dB. For N = 16 and per-channel power of -130 dBm at the amplifier: total = -130 + 12 = -118 dBm, well below the JPA P1dB of -100 dBm. (3) Room-temperature demodulation errors: imperfect digital filtering between closely-spaced channels. These effects are manageable with careful design and are far outweighed by the cabling and thermal benefits of multiplexing.