The millikelvin stack explained — 300K to 10mK in seven stages

A transmon qubit at room temperature is just a small piece of patterned aluminium and niobium on a silicon wafer. It only becomes a qubit when you cool it past the point where thermal noise stops drowning the quantum signal — and that cooling is not a single step. It's seven. Each stage of a dilution refrigerator does a specific job, and if any one of them is misbehaving, the qubit upstairs doesn't care how clever your control electronics are. This is the part of quantum computing that nobody puts on a slide, so let's walk it properly.

Why 10 millikelvin, and not 1 kelvin or 100 microkelvin

The number that matters for a superconducting transmon is the ratio between the qubit's transition energy and the thermal energy of its environment. Transmon frequencies sit around 4–6 GHz. Convert that to temperature via hf/k_B and you get something in the low hundreds of millikelvin. To keep the qubit in its ground state with high probability — say, well above 99% — you need the surrounding bath an order of magnitude colder than that energy scale. Ten millikelvin gives you headroom. It also matches the operating range where dilution refrigerators are most efficient: the dilution process itself runs out of cooling power much below about 7 mK without exotic tricks.

Going colder than 10 mK doesn't help the qubit much and costs you a lot. Going warmer means residual thermal photons in the readout line start exciting the qubit, and your T_1 measurements stop reflecting the chip and start reflecting your fridge hygiene. So 10 mK is not arbitrary — it's the sweet spot where the physics, the engineering, and the electricity bill all agree.

Stage 1: 300 K to 50 K — the pulse tube's first lift

The outermost stage of a modern dry dilution fridge is the first stage of a pulse-tube cryocooler. It uses oscillating high-pressure helium gas — driven by a compressor that sits in a separate room because it's loud and warm — to move heat from the 50 K plate up to ambient. The pulse tube replaces the wet liquid-helium baths older fridges used, which is why we can run these systems continuously for months instead of refilling cryogens every few days.

The 50 K stage is mostly a thermal shield. Everything inside it is wrapped in many layers of aluminised mylar — superinsulation — to block radiative heat from the room-temperature vacuum can. Cabling makes its first big thermal anchor here. Every coaxial line carrying microwave control or readout signals down to the chip is heat-sunk to this plate, because copper at room temperature is a thermal highway and you cannot afford to dump 300 K of conducted heat onto colder stages downstream.

Stage 2: 50 K to 4 K — the workhorse plate

The pulse tube's second stage takes you to about 4 K, the temperature of liquid helium at atmospheric pressure. This is where most of the active electronics inside the fridge live. Cryogenic low-noise amplifiers — typically high-electron-mobility-transistor (HEMT) devices — are mounted here for the readout chain. They're warm enough to dissipate a few milliwatts each without trouble, and cold enough that their input noise temperature is in the single-kelvin range, which is what you need to amplify single-photon-level readout signals without burying them.

The 4 K plate is also where you put the bulk of your attenuation on the input lines. Drive lines coming down from room-temperature arbitrary waveform generators carry not just the signal you want but the Johnson noise of every resistor between here and there. You attenuate aggressively — often 20 dB at this stage — which knocks the noise down along with the signal. You make up the signal loss by driving harder from the top.

Stage 3: 4 K to ~800 mK — the still

Below 4 K, the pulse tube can't help you. From here down, you're using the dilution unit itself, and the first plate of that unit is called the still. It runs at roughly 600–900 mK. The still does two jobs. First, it's another thermal anchor stage for cables and another opportunity for attenuation. Second — and this is the clever bit — it's where the dilution fridge's internal pump works.

A dilution fridge runs on a mixture of helium-3 and helium-4. Below about 870 mK, that mixture spontaneously separates into two phases: a concentrated phase that's almost pure helium-3, and a dilute phase that's mostly helium-4 with about 6.6% helium-3 dissolved in it. The still selectively boils helium-3 out of the dilute phase, because helium-3 has a higher vapour pressure at these temperatures. That vapour gets pumped away, condensed, and re-injected into the concentrated phase elsewhere in the fridge. The cycle is continuous.

Stage 4 and 5: the cold plate and the heat exchangers

Between the still and the mixing chamber sit the cold plate (around 100 mK) and a series of counterflow heat exchangers. These are the unglamorous plumbing of the fridge, and they're where the real engineering lives. Incoming concentrated helium-3 — relatively warm from being pumped and recondensed upstairs — needs to be pre-cooled before it reaches the mixing chamber, otherwise it dumps heat exactly where you don't want it.

The heat exchangers do this by running the warm incoming stream against the cold outgoing stream in opposite directions, transferring heat across thin sintered-silver surfaces. Sintered silver gives you enormous surface area in a small volume, which matters because at these temperatures the Kapitza thermal boundary resistance between liquid and metal becomes dominant. A poorly designed heat exchanger is the most common reason a dilution fridge fails to reach base temperature. The cold plate itself is another cabling anchor and a structural mounting point for components like circulators and isolators in the readout chain.

Stage 6: the mixing chamber at 10 mK

The mixing chamber is where cooling actually happens. The phase boundary between concentrated and dilute helium-3 sits inside this chamber. When a helium-3 atom crosses from the concentrated phase into the dilute phase, it absorbs energy — analogous to evaporative cooling, except the "vapour" is helium-3 dissolved in superfluid helium-4 rather than gas. This is the one cooling process in the entire stack that keeps working efficiently below 100 mK, and it's why dilution refrigerators exist.

The mixing chamber plate is the coldest large surface in the fridge. The qubit chip is mounted to it, usually inside a light-tight, magnetically shielded sample holder. "Light-tight" is not a metaphor — a single stray infrared photon from a warmer stage can break Cooper pairs in your superconducting circuits and ruin coherence. The shielding stack typically includes mu-metal for low-frequency magnetic fields, a superconducting niobium or aluminium can for residual flux pinning, and a layer of infrared-absorbing coating inside the innermost can.

Stage 7: the chip and its immediate environment

The seventh stage is the qubit package itself. The plate reads 10 mK, but the chip can be warmer. Microwave drive pulses dissipate energy on-chip. Two-level-system defects in the substrate and oxide layers absorb and re-emit photons. The bond wires connecting the chip to its PCB are themselves a thermal path. Getting the effective electron temperature of the qubit close to the bath temperature is its own problem, and it's measurable: you fit the equilibrium population of the excited state and back out an effective T. A well-built system gets the qubit to within a factor of two or three of the plate temperature. A poorly built one sits at 50 mK while the plate proudly reads 8.

This is also where filtering matters most. Every line entering the package passes through low-pass filters, often eccosorb-based, to kill stray high-frequency radiation. Infrared filtering is non-negotiable. The package is the last line of defence, and if you've done everything right upstream, it's where the system stops being plumbing and starts being a quantum computer.

What this means for the machine we're building

The cryogenic stack is the part of Ireland Quantum 100 that has the longest lead time and the least room for cleverness. You can iterate on control electronics in software. You cannot iterate on a dilution refrigerator after it's installed — every cable, every filter, every thermal anchor has to be right before you close the cans and start the cooldown, because a full warm-up-to-fix-something cycle is measured in weeks. This is why our site fit-out and cryostat install are sequenced ahead of any qubit work, and why the delivery roadmap looks the way it does.

It's also why dilution-fridge capacity, not qubit count, is the real bottleneck for sovereign quantum compute in Europe. Building chips is hard. Building the millikelvin environment to run them in, repeatably, with the wiring density a useful processor needs, is harder.

Where to start if you're new to this

If you're an engineer trying to get your head into the cryogenics quantum stack for the first time, skip the marketing material and read two things: the Bluefors and Oxford Instruments technical manuals for their dilution units, both freely available, and Frank Pobell's Matter and Methods at Low Temperatures. Between them you'll have a working mental model of every stage above. After that, the right thing to do is to find a lab running a system and ask if you can watch a cooldown. Two days at a fridge teaches you more than a month of papers.