Why are cryogenic attenuators needed on qubit drive lines?

Room-temperature electronics (signal generators, AWGs) produce thermal noise with a noise temperature of 300 K across the full bandwidth. This noise, if delivered directly to a qubit operating at 10 mK with a transition frequency of 5 GHz, would cause continuous excitation and decoherence. The thermal photon occupation at 5 GHz and 300 K is n = 1/(exp(hf/kT)-1) = approximately 1250 photons, while at 10 mK it is approximately 0.0001. Attenuators at each thermal stage reduce the noise: a 20 dB attenuator at 4 K reduces the 300 K noise by a factor of 100 but adds its own thermal noise at 4 K (n approximately 17). A second 20 dB attenuator at the mixing chamber (10 mK) reduces the 4 K noise by another factor of 100 and adds negligible noise at 10 mK. The total input line attenuation is typically 60 to 70 dB (20 dB at 4 K, 20 dB at still/CP stage, 20 dB at MXC), ensuring that noise at the qubit is dominated by the physical temperature of the coldest stage rather than room-temperature thermal noise.

What materials are used for cryogenic coaxial cables?

Three material systems dominate. Cupronickel (CuNi, 70Cu-30Ni alloy) has thermal conductivity approximately 25 times lower than copper at 4 K, making it the workhorse for cryogenic wiring where thermal isolation is important. It introduces RF loss of approximately 1 to 3 dB per meter at 5 GHz (acceptable for input lines where attenuators add much more). Niobium-titanium (NbTi) is a superconductor below 9.2 K with near-zero RF loss and very low thermal conductivity (approximately 0.1 W/mK at 4 K). NbTi cables are used for the output (readout) lines from the mixing chamber to the 4 K stage, where preserving the weak qubit signal is critical. Beryllium-copper (BeCu) provides moderate thermal conductivity and moderate RF loss, used for intermediate stages. Standard semi-rigid copper cables (UT-085, UT-141) are used only at the room-temperature stage. Dielectric materials include PTFE (stable to 4 K) and silicon dioxide (for thin-film on-chip transmission lines at millikelvin temperatures).

How does the thermal budget work in a dilution refrigerator?

A dilution refrigerator has 4 to 6 thermal stages, each with a specific cooling power: 50 K plate (30 to 50 W), 4 K plate (1 to 2 W from pulse tube cooler), still plate at 700 mK (20 to 40 mW), cold plate at 100 mK (500 microW), and mixing chamber at 10 to 20 mK (10 to 20 microW). Every coaxial cable connecting these stages conducts heat from the warmer to the colder stage according to Q = integral of kappa(T) * A/L dT, where kappa is thermal conductivity, A is cross-sectional area, and L is length. For a single UT-085 CuNi cable from 4 K to 10 mK (0.5 m length): heat leak is approximately 0.5 microW. With 200 coaxial lines (typical for a 100-qubit system), total cable heat leak at the MXC is 100 microW, consuming 50 to 100% of the available cooling power. This is why cable material and diameter selection is critical: switching from CuNi to NbTi below 4 K reduces heat leak by a factor of 5 to 10. Reducing cable diameter from UT-085 to UT-047 halves the cross-section and heat leak.

Quantum Computing RF

Coaxial Wiring Cryogenic

/koh-ak-see-ul wy-ring kry-oh-jen-ik/

Cryogenic coaxial wiring carries microwave signals (4 to 8 GHz) from 300 K to 10 mK in dilution refrigerators for quantum computing, astronomy, and particle physics. Uses NbTi (superconducting, near-zero RF loss below 9.2 K), CuNi (25x lower thermal conductivity than Cu), and BeCu. Cryogenic attenuators (20 dB/stage) reduce 300 K thermal noise from ~1,250 photons to <0.001 at the qubit. Total input line: 60 to 70 dB attenuation across 4 to 6 thermal stages.

Category: Quantum Computing RF

Temperature: 300 K to 10 mK

Attenuation: 60 to 70 dB total

Understanding Cryogenic Coaxial Wiring

Superconducting quantum processors operate at temperatures of 10 to 20 millikelvin inside dilution refrigerators, but the control electronics (microwave sources, digitizers, FPGA controllers) remain at room temperature. Bridging this 300 K to 10 mK temperature gap with RF-quality coaxial cables that preserve signal integrity while minimizing heat leak is one of the most critical engineering challenges in scaling quantum computers. Each qubit requires at least 2 coaxial lines (drive and readout), so a 1,000-qubit processor needs 2,000+ cryogenic cables, each contributing heat load to stages with only microwatts of cooling power.

The design challenge is a three-way optimization: signal transmission quality (low RF loss for readout lines, high attenuation for drive lines), thermal isolation (low thermal conductivity to minimize heat leak), and mechanical robustness (cables must survive hundreds of thermal cycles from 300 K to 10 mK without breaking or degrading). No single cable material satisfies all three requirements, so cryogenic wiring uses a segmented approach: different cable materials at each thermal stage, connected by attenuators, filters, and cryogenic connectors (SMA, SMPM, or custom blind-mate). The input (drive) line prioritizes thermal noise reduction through heavy attenuation, while the output (readout) line prioritizes low loss to preserve the weak qubit state-dependent signal for amplification by a quantum-limited amplifier (TWPA or JPA) at the 4 K stage.

Cryogenic Wiring Equations

Thermal Noise Photon Number:
n = 1 / (e^hf/kT - 1)

Heat Leak Through Cable:
Q = (A/L) × ∫ κ(T) dT (W)

Noise After Attenuation:
T_eff = T_in/G + T_atten(1 - 1/G)

Where h = Planck's constant, f = frequency, k = Boltzmann's, T = temperature, A = cable cross-section, L = length, κ = thermal conductivity, G = attenuator power gain (<1). At 5 GHz: n(300K) = 1,250; n(4K) = 17; n(10mK) = 0.0001.

Cryogenic Cable Materials

Material	κ at 4K (W/mK)	RF Loss (dB/m, 5 GHz)	Stage	Role
Copper (UT-085)	400	0.5	300 K only	Room-temp connections
BeCu	10	2 to 3	300 K to 50 K	Intermediate stages
CuNi (70/30)	15	1 to 3	50 K to 4 K	Input drive lines
NbTi	0.1	≈0 (superconducting)	4 K to 10 mK	Output readout lines
Stainless steel	0.3	5 to 10	DC lines	Bias, flux lines

Common Questions

Frequently Asked Questions

Why are cryogenic attenuators needed?

Room-temp noise at 5 GHz: ~1,250 photons (300 K). 20 dB at 4 K reduces by 100x, adds 4 K noise (~17 photons). 20 dB at 100 mK: reduces by 100x again, adds negligible noise. 20 dB at 10 mK: final stage. Total 60 to 70 dB ensures qubit noise is dominated by 10 mK physical temperature (~0.0001 photons).

What materials are used?

CuNi: workhorse, 25x lower κ than Cu, 1 to 3 dB/m loss at 5 GHz. NbTi: superconducting below 9.2 K, near-zero RF loss, 0.1 W/mK at 4 K; used for output lines. BeCu: moderate performance, intermediate stages. Cu: room temp only. PTFE dielectric stable to 4 K. Stainless steel for DC bias lines.

How does the thermal budget work?

MXC cooling: 10 to 20 μW at 10 mK. Single UT-085 CuNi cable (4 K to 10 mK, 0.5 m): ~0.5 μW heat leak. 200 lines (100-qubit system): 100 μW total, consuming 50 to 100% of cooling power. Mitigations: NbTi below 4 K (5 to 10x reduction), smaller diameter (UT-047 halves cross-section), and cable thermalization at each stage.

Related Terms

← Coaxial Termination Cob →