Why 10 millikelvin, and how helium gets you there
A superconducting qubit rings at a few gigahertz. The problem is that ordinary room-temperature heat is a constant drumbeat of random energy, and at room temperature that drumbeat is far louder than a single one of the qubit's microwave quanta — so heat would flip the qubit over and over before you could compute anything. The fix is brute and physical: take the heat away. Cool the chip to roughly 10 millikelvin, about a hundredth of a degree above absolute zero, and the thermal drumbeat finally falls quieter than the qubit's own energy. Only then can a quantum state sit still long enough to be useful.
Ordinary fridges and even liquid helium can't reach that low on their own. A dilution refrigerator gets there with a clever trick involving two isotopes of helium: helium-3 and helium-4. Below about 0.87 kelvin a liquid mixture of the two separates into two layers, like oil floating on water. Pumping helium-3 atoms across the boundary from the rich layer into the dilute layer costs energy, and that energy is dragged out as heat from whatever the mixing chamber touches — the same way sweat cools your skin as it evaporates, just colder and continuous. As long as the pumps keep running, the cold keeps flowing.
thermal energy k_B * T vs qubit photon h * f
at T = 10 mK : k_B*T ~ 0.21 GHz
qubit : h*f ~ 5 GHz
0.21 GHz << 5 GHz -> random heat can no longer easily
flip the qubit. that gap is the
whole reason for going to mK.The stages: an onion of plates, each colder than the last
A dilution fridge is built as a stack of metal plates, each one colder than the plate above it, hanging like a chandelier. Heat does not vanish in one jump from room temperature to 10 millikelvin; it is shed gradually, plate by plate, on the way down. A useful set of labels — they vary between machines — runs roughly: a 50-kelvin plate, a 4-kelvin plate, the still at around 0.8 kelvin, a cold plate near 0.1 kelvin, and the mixing chamber at base where the chip actually lives. Every signal wire and coax line threads through all of them.
The number that matters most for chip design is in the right-hand column below: cooling power, how much heat each plate can pump away per second. Read down it and one fact jumps out — the colder the plate, the less heat it can remove. The 4-kelvin plate can shrug off something like a watt; the mixing chamber at base copes with only a few hundred microwatts, a millionth of that scale. (Exact figures vary by model; these are honest order-of-magnitude numbers, not a spec sheet.)
STAGE TEMPERATURE COOLING POWER (order of magnitude)
------------------ ------------------ ---------------------------------
room ~300 K (the warm world; not cooled)
50 K plate ~50 K a few watts
4 K plate ~4 K ~1 watt
still ~0.8 K ~tens of milliwatts
cold plate ~0.1 K ~hundreds of microwatts
mixing chamber ~0.01 K (10 mK) ~hundreds of microwatts or less
^^^ the chip lives here ^^^
rule of the stack: colder plate -> far less cooling power.Why every input line is deliberately weakened
Here is the awkward thing about wires: the same coax that carries your control pulse down to the qubit also carries thermal noise the other way — a faint trickle of warm, random microwave photons leaking down from the room above. Even a handful of those stray photons would scramble a qubit. So designers do something that sounds backwards: they throw the signal away on purpose. Cryogenic attenuation means bolting small attenuators onto the input line at each cold plate, weakening the pulse — and, crucially, weakening the warm noise riding alongside it.
Why does weakening the signal clean it? An attenuator is just a resistor network. It absorbs most of the power passing through, then re-emits only the gentle thermal noise of its own temperature. So an attenuator bolted to the 4-kelvin plate replaces room-temperature noise with 4-kelvin noise; another near the chip replaces that with millikelvin noise. Stage by stage, each plate hands the next a colder, quieter signal, and the heat the attenuator absorbs gets dumped onto a plate the fridge can actually cool. Your pulse arrives faint but bathed in near-perfect quiet.
room (300 K) ---[ -20 dB @ 4K ]---[ -20 dB @ mK ]--- qubit
| | |
noisy pulse warm noise millikelvin
+ warm noise replaced by noise only:
4 K noise very quiet
a common starting split is ~20 dB at 4 K and ~20 dB near
the chip, but the exact numbers are tuned per fridge,
per line -- there is no single right answer.The thermal budget: the wall that scaling hits
Now put the two halves together. The bottom plate can remove only a few hundred microwatts, and every cable, attenuator, amplifier, and filter you add dumps some heat onto a plate. The cryogenic thermal budget is simply the accountant's view of this: on each plate, the heat conducted down the wires plus the heat dissipated right there, summed over every line, must stay under what that plate can pump away. Cross the line and the whole stage warms up and the qubit stops working.
A handful of qubits is easy. The budget only bites when you imagine thousands of control and readout lines crowding into the same cold stages: you cannot just add more wires, because the coldest plates run out of cooling power long before you run out of physical room. This is one of the real, unglamorous walls in scaling quantum chips — and it is why so much current work goes into cryo-CMOS control chips inside the fridge, into multiplexed readout that packs more qubits per line, and into shrinking bulky components. All promising, all still early.
Reaching base temperature is necessary but not sufficient. Once the chip is cold and the lines are quiet, what still limits the qubit is loss in the materials themselves — and there is a tidy way to bookkeep it. The chip's quality, its internal quality factor Q_i, falls when the qubit's electric field overlaps lossy stuff: surface oxides, interfaces, stray defects. The formula below splits that into a *participation ratio* (how much of the field sits in each region) times that region's *loss tangent* (how lossy the region is). Cold is the price of entry; clean materials are how you actually win.
1 / Q_i = sum over regions of ( p_region * tan_delta_region )
where
p_region = participation ratio: fraction of the qubit's
electric-field energy stored in that region
tan_delta_region= loss tangent: how lossy that material is
read it plainly:
* a region only hurts if BOTH p and tan_delta are non-trivial
* shrink p (keep the field out of bad surfaces) OR
shrink tan_delta (use cleaner materials) to raise Q_i
* higher Q_i -> energy leaks away more slowly -> better qubit
note: always check the drive power -- a Q_i quoted at high power
can be many times the single-photon Q_i a qubit actually lives with.