Effective temperature of a superconducting qubit

Short answer: A superconducting qubit that is cooled in a dilution refrigerator still has a small chance of being found in its excited state, which sets an effective temperature. A 2015 Physical Review Letters paper reports that a 3D transmon followed a thermal distribution from 35 to 150 mK and saturated at about 0.1% excited-state population below 35 mK, giving an effective temperature of 35 mK. This is one experiment and one set of devices.

The question

The abstract begins by noting remarkable advances in coherence and control fidelity for cryogenic solid-state qubits. It then says that thermalizing such devices to their milliKelvin environments has remained a long-standing fundamental and technical challenge. If a qubit is not in thermal equilibrium with the cold stage, it starts experiments partly excited, which adds error before any gate is applied.

What the authors measured

The authors present a systematic study of the first-excited-state population of a 3D transmon superconducting qubit mounted in a dilution refrigerator whose temperature could be varied. They used a modified version of a protocol developed by Geerlings and coauthors. Over the temperature range 35 to 150 mK, they observe the excited-state population to be consistent with a Maxwell-Boltzmann distribution, meaning the qubit was in thermal equilibrium with the refrigerator. Below 35 mK, the population saturates at approximately 0.1%.

A cross-check

They verified the saturation with a flux qubit that had a ten times stronger coupling to its readout resonator. That is a different kind of device and a different readout coupling, which makes it less likely that the saturation comes from the readout of one device alone. From the saturation level, the authors conclude that these qubits have an effective temperature of 35 mK.

What might set the floor

The authors consider one possible explanation. Assuming the effective temperature is due solely to hot quasiparticles, they infer a qubit lifetime of 108 microseconds. They say this is in plausible agreement with the measured 80 microseconds. This is a consistency check under an assumption, not proof that quasiparticles are the only cause.

Reading the numbers

The 0.1% figure is small, but it matters because it is a floor: cooling the refrigerator further below 35 mK did not lower the qubit's excited-state population. That is the reason the authors describe an effective temperature that differs from the refrigerator temperature at the cold end. The thermal behavior above 35 mK is the reassuring part, since it shows the qubit and its readout are measuring a real equilibrium population. The behavior below it is the open question the paper highlights.

Limits

The study covers a 3D transmon and a flux qubit in specific setups. A saturation at 0.1% describes those experiments, and the abstract does not say it applies to other qubit designs or other laboratories. The explanation about quasiparticles is conditional. A third listed source was a library page that carried the same abstract and adds no independent evidence.

FAQ

What is an effective qubit temperature?

The temperature that would give the measured excited-state population if the qubit were in thermal equilibrium.

Where does the thermal behavior stop?

Below 35 mK, where the excited-state population saturates at about 0.1%.

Was the result checked on another device?

Yes, with a flux qubit having ten times stronger readout coupling.

Does this prove quasiparticles cause the floor?

No. The authors say the inferred lifetime of 108 microseconds plausibly agrees with the measured 80 microseconds if the floor is due solely to hot quasiparticles.

Why does it matter?

An excited qubit at the start of an experiment adds error before gates run.