Cryostat Wiring Bottleneck

Chip Scale

Qubit count 300

Coax lines / qubit 3.0

Wiring Loom

Stage Heat Load vs. Budget

4 K stage0 / 1500 mW

Still (~0.8 K)0 / 10 mW

Cold plate (~100 mK)0 / 500 µW

Mixing chamber (~10 mK)0 / 20 µW

Base temp T_MXC

10.0 mK

Thermal photons n̄

3e-11

Total coax lines

900

Max qubits in budget

—

Qubits coherent

How it works

A dilution refrigerator cools a superconducting-qubit chip through cascaded stages (50 K → 4 K → still ≈0.8 K → cold plate ≈100 mK → mixing chamber ≈10 mK). Every qubit needs its own coax lines in and out (drive, flux bias, readout), and each line is a physical thermal short between stages: heat flows down it by conduction,

Q_stage = N_lines × q(material, stage)   [µW per stage]

where q is the conducted heat per line, tabulated per stage and cable type below. Stainless-steel semi-rigid coax conducts far more heat than NbTi, which becomes superconducting (and a poor phonon conductor) below its ~9.2 K critical temperature — real cryostats mix both, using NbTi only for the coldest runs.

Each stage has a finite cooling power budget (its refrigerator's capacity at that temperature). If the wiring's heat load exceeds the mixing-chamber budget Q₀ at its design temperature T₀, the stage settles at a higher equilibrium temperature, since a dilution unit's cooling power scales roughly as T²:

T_MXC = T₀ · √(max(1, Q_load / Q₀))

A hotter mixing chamber means more thermal photons in each qubit's readout resonator, given by the Bose–Einstein occupation at the qubit frequency f (here 5 GHz):

n̄(T) = 1 / (exp(hf / k_BT) − 1)

Once n̄ climbs past roughly 0.005–0.05 the qubit's effective T1/T2 collapses — this is the real "wiring bottleneck" that limits how many physical qubits a single fridge can host, and why frequency-multiplexed readout (packing several qubits onto one output line) and NbTi harnesses are standard scaling techniques.

Qubit count / lines per qubit — sets the total coax line count threading the fridge.
Stainless steel vs. NbTi — swaps the conduction table for stages below 4 K.
Freq-mux readout — cuts effective line count ~60%, modelling shared readout lines.

Coax wiring Coherent qubit Decohered qubit

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