What is the role of a cryogenic circulator in the readout chain of a superconducting quantum processor?
Cryogenic Circulators for Quantum Systems
Circulators are among the most critical and problematic components in quantum computing cryostats. They are bulky, heavy, contain ferrite materials that produce stray magnetic fields, and their performance depends on temperature, making them a significant engineering challenge at scale.
Operating Principle at Cryogenic Temperatures
Circulators use ferrite materials (yttrium iron garnet, YIG) biased by a permanent magnet that creates a non-reciprocal Faraday rotation of the RF signal. The magnetic bias establishes a preferred circulation direction. At cryogenic temperatures, the ferrite properties change: saturation magnetization increases, linewidth narrows, and the optimal bias field shifts. Cryogenic circulators are specifically designed (or re-biased) for operation at 4K or below. Common cryogenic circulators: Quinstar (QCY series), Low Noise Factory (LNF-CIC series), Raditek (RADC series), and custom-built units from quantum hardware labs. The LNF-CIC4_8A covers 4-8 GHz with 0.3 dB insertion loss and 20 dB isolation at base temperature, and is one of the most widely used in the quantum computing community.
Isolation Requirements
The required isolation depends on the amplifier noise and qubit sensitivity. A HEMT amplifier at 4K with noise temperature T_N = 3K has noise power of kT_N × B = 4.1 × 10^-23 × B watts/Hz. For a 10 MHz readout bandwidth: -104 dBm of noise power. If this reaches the qubit with only 20 dB of isolation, the qubit sees -124 dBm of noise, corresponding to approximately 0.1 photons at 6 GHz, which can cause measurable dephasing. With 60 dB of isolation (3 circulators): the qubit sees -164 dBm, well below the single-photon level, reducing amplifier-induced dephasing to negligible levels. When using a quantum-limited amplifier (JPA/TWPA) as the first stage, its gain (20 dB) reduces the contribution of subsequent HEMT noise, but the JPA itself generates quantum noise at the single-photon level that must still be isolated from the qubit.
Scaling Challenges
Each readout line requires 2-3 circulators, each approximately 15×15×10 mm and weighing 10-20 grams. For a 1000-qubit system with 200 readout lines: 400-600 circulators occupying significant volume and mass at the MC stage. The ferrite in each circulator produces a stray magnetic field of 1-10 mT at 1 cm distance, requiring mu-metal or cryoperm magnetic shielding around each unit or the entire qubit package. Alternative approaches under development: (1) On-chip circulators using Josephson junction arrays (non-reciprocal transmission without ferrites, demonstrated in labs at limited bandwidth). (2) Directional amplifiers that combine amplification and circulation functions. (3) Multiplexed readout that reduces the number of output lines (and therefore circulators) by reading multiple qubits through a single line.
S12 = S23 = S31 = 0 (isolation)
Isolation (dB) = -20·log₁₀|S12|
Total Isolation = N × isolation_per_unit
Back-action noise at qubit: P_BA = P_amp_noise - Isolation_total
Frequently Asked Questions
Why not use isolators instead of circulators?
Isolators are two-port devices (circulators with port 3 internally terminated). They provide the same isolation as a circulator but with one fewer accessible port. In practice, circulators are preferred because: (1) the third port allows flexible routing (useful for pump tones in parametric amplifier setups). (2) Circulators with external 50-ohm terminations are easier to troubleshoot (you can disconnect the load and test each port). (3) Some readout architectures use the third port for signal injection. In positions where only isolation is needed, isolators save minor space but are functionally equivalent.
How does magnetic shielding affect nearby qubits?
Stray magnetic fields from circulator permanent magnets can penetrate superconducting qubits and cause flux noise, reducing T2 coherence time. Transmon qubits are relatively insensitive to uniform magnetic fields (first-order flux-insensitive at the sweet spot), but field gradients and time-varying fields still cause dephasing. Mitigation: (1) Mu-metal or cryoperm shields around each circulator (reduces stray field by 20-40 dB). (2) Physical separation: mount circulators at least 5-10 cm from the qubit package. (3) Orient circulator magnets to minimize field at the qubit location. (4) Use superconducting magnetic shields (Nb cans) around the qubit chips to expel external fields via the Meissner effect.
What bandwidth do cryogenic circulators cover?
Standard cryogenic circulators cover 4-8 GHz (one octave), matching the typical transmon qubit frequency range. Wideband models cover 4-12 GHz for systems with higher-frequency qubits or wider readout frequency spans. For multiplexed readout (8-16 qubits per readout line), the circulator bandwidth must span the full range of readout resonator frequencies, which may span 1-2 GHz. If the readout frequencies exceed the circulator bandwidth, multiple circulator models or custom-designed wideband circulators are needed. The insertion loss of wideband circulators is typically 0.1-0.2 dB higher than narrowband designs.