How is the heat load budget managed at the mixing chamber cold plate?

The heat load budget at the MXC plate is typically 10 to 20 microwatts for a system with 50 to 100 qubits. Sources include conducted heat through RF cables (mitigated by using NbTi coax and multi-stage attenuation), DC bias lines (filtered through copper powder filters and thermally anchored at each stage), radiated heat through infrared leaks in the radiation shields, and dissipation from cryogenic amplifiers (HEMT amplifiers are mounted at 4 K, not at MXC). Careful thermal design allocates roughly 5 microwatts for cable conduction, 3 microwatts for radiation, and reserves 5 to 10 microwatts for margin and future scaling.

Quantum Computing RF

Cold Plate (Quantum)

Q: What temperatures do the cold plates in a dilution refrigerator reach?

A typical dilution refrigerator has five to six thermally isolated stages. The 50 K and 4 K plates are cooled by a pulse-tube cryocooler. The still plate operates at 700 to 900 mK, the cold plate (or intermediate plate) at 50 to 100 mK, and the mixing chamber plate at 10 to 20 mK. The mixing chamber plate, often called the base plate or MXC plate, is where superconducting qubit chips are mounted. Each stage intercepts conducted and radiated heat from warmer stages, with the total cooling power at the MXC ranging from 10 to 500 microwatts at 20 mK depending on the refrigerator model.

Q: Why is thermal anchoring of RF lines critical at millikelvin temperatures?

Every RF coaxial cable running from room temperature to the mixing chamber conducts heat proportional to its thermal conductivity and the temperature gradient. A standard stainless steel SMA cable conducts approximately 0.5 mW from 300 K to 4 K, which is manageable, but even 1 microwatt of heat leak at the 20 mK stage can overwhelm the refrigerator's cooling power. Engineers use NbTi superconducting coax or CuNi coax below 4 K, thermally anchor the outer conductor at each temperature stage, and install cryogenic attenuators (20 to 40 dB total) that both attenuate thermal noise photons and thermalize the center conductor. Without proper anchoring, the qubit environment warms above 50 mK and coherence times drop by 10 to 100 times.

/kohld playt/

A thermally regulated copper or gold-plated mounting stage inside a dilution refrigerator, operating at 10 to 20 mK, where superconducting qubit chips, quantum-limited parametric amplifiers, and microwave control/readout lines are thermally anchored. The cold plate provides the sub-100 mK environment required for transmon and flux qubit coherence times exceeding 100 μs by suppressing thermal photon occupation to below 0.01 at qubit frequencies of 4 to 8 GHz. A typical dilution refrigerator has five to six temperature stages (50 K, 4 K, 900 mK, 100 mK, 20 mK), each with a dedicated cold plate that intercepts conducted and radiated heat loads from warmer stages. The mixing chamber plate provides 10 to 500 μW of cooling power at 20 mK.

Category: Quantum Computing RF

Base Temperature: 10 to 20 mK

Cooling Power: 10 to 500 μW at 20 mK

Understanding Cold Plate (Quantum)

Superconducting qubits operate at microwave frequencies (4 to 8 GHz) where the thermal photon occupation number n_th = 1/(e^hf/kT - 1) must be far below 1 to avoid thermally induced decoherence. At 5 GHz, n_th drops below 0.01 only when the temperature falls below approximately 50 mK. The mixing chamber cold plate of a dilution refrigerator reaches 10 to 20 mK, providing a comfortable margin. The cold plate itself is machined from OFHC (oxygen-free high-conductivity) copper and gold-plated to prevent oxidation, with bolt-on mounting positions for qubit packages, microwave isolators, cryogenic attenuators, and low-pass filters.

The thermal design challenge is managing heat loads at each stage. Every RF coaxial cable, DC bias line, and mechanical support conducts heat from warmer stages. Engineers use progressively lower thermal-conductivity materials at colder stages: stainless steel coax from 300 K to 4 K, then CuNi or NbTi superconducting coax from 4 K to 20 mK. Cryogenic attenuators (typically 20 dB at 4 K and 20 dB at the still plate) serve dual purposes: attenuating room-temperature thermal noise photons and thermalizing the cable center conductor at each stage. The total attenuation of 40 to 60 dB reduces the effective noise temperature at the qubit to below 50 mK.

Thermal Photon Occupation and Heat Conduction

Thermal Photon Number:
n_th = 1 / (e^hf/k_BT − 1)

Heat Conduction Through Cable:
Q = (κA / L) × (T_hot − T_cold)

Dilution Refrigerator Cooling Power:
Q_MXC = 84 ṅ₃ (T_MXC² − T_still²)

Where h = Planck's constant, f = qubit frequency, k_B = Boltzmann constant, T = temperature (K), κ = thermal conductivity, A = cross-section area, L = cable length, ṅ₃ = He-3 circulation rate (mol/s). At 5 GHz, n_th = 0.006 at 20 mK vs. 0.65 at 100 mK.

Dilution Refrigerator Stage Comparison

Stage	Temperature	Cooling Power	RF Components Mounted	Cable Material
50 K plate	40 to 50 K	30 to 40 W	IR filters, radiation shield	Stainless steel coax
4 K plate	3 to 4.5 K	1 to 1.5 W	HEMT amplifier, isolators	Stainless steel coax
Still plate	700 to 900 mK	20 to 30 mW	Attenuators, filters	NbTi or CuNi coax
Cold plate	50 to 100 mK	200 to 500 μW	Attenuators, DC filters	NbTi coax
MXC plate	10 to 20 mK	10 to 500 μW	Qubit chip, JPA, circulators	NbTi coax

Common Questions

Frequently Asked Questions

What temperatures do the cold plates in a dilution refrigerator reach?

A typical dilution refrigerator has five to six stages. The 50 K and 4 K plates are cooled by a pulse-tube cryocooler. The still plate operates at 700 to 900 mK, the cold plate at 50 to 100 mK, and the mixing chamber plate at 10 to 20 mK. The MXC plate is where qubit chips are mounted, with total cooling power of 10 to 500 μW at 20 mK depending on the refrigerator model and He-3 circulation rate.

Why is thermal anchoring of RF lines critical at millikelvin temperatures?

Every coaxial cable conducts heat proportional to its thermal conductivity and temperature gradient. Even 1 μW of heat leak at 20 mK can overwhelm the refrigerator. Engineers use NbTi superconducting coax below 4 K, thermally anchor outer conductors at each stage, and install cryogenic attenuators (20 to 40 dB total) to attenuate thermal noise and thermalize center conductors. Without proper anchoring, the qubit environment warms above 50 mK and coherence times drop by 10 to 100 times.

How is the heat load budget managed at the mixing chamber?

The MXC heat budget is typically 10 to 20 μW for 50 to 100 qubit systems. Sources include cable conduction (mitigated with NbTi coax and multi-stage attenuation), DC bias lines (filtered through copper powder filters and anchored at each stage), infrared radiation through shield leaks, and amplifier dissipation (HEMT amps are at 4 K, not MXC). Typical allocation: 5 μW cable conduction, 3 μW radiation, 5 to 10 μW margin for scaling.

Related Terms

← Cold Load Cold Plate (Thermal) →