Bigger Than a Breadbox, Smaller than a Football Stadium
[Second in the "practicalities of scalable quantum computers" series. The first installment was Forty Bucks a Qubit. Third is How Many Qubits Can Dance on the Head of a Pin?]
After talking to various people, I'm raising the target price on my quantum computer to a hundred million dollars. The U.S. government clearly spends that much on cluster supercomputers, though I don't think that they reached that level in the heyday of vector machines. BlueGene, for example, built by IBM, has 131,072 processors (65536 dual-core), and there's no way you're going to build a system like that, counting packaging, power, memory, storage, and networking, for less than a grand a processor (all these prices are ignoring physical plant, including the building).
Let's talk about packaging, cooling, and housing a semiconductor-based quantum computer. Even though we're talking about manipulating individual quanta, the space, power, thermal, and helium budgets for this are large. Helium? Yeah, helium. Both superconducting qubits and quantum dot qubits are operated at millikelvin temperatures, and the way you get there is by using a dilution refrigerator.
A dilution refrigerator, or dil fridge, uses the different condensation characteristics of helium-3 and helium-4 to cool things down to millikelvin temperatures. See the web pages here, here, and here, and the excellent PDF of the Hitchhiker's Guide to the Dilution Refrigerator from Charlie Marcus' lab at Harvard. All of the dil fridges I have ever seen are from Oxford Instruments.
Although there are a bunch of models, all the ones I've seen are almost two meters tall and a little under a meter in diameter, and you load your test sample in from the top on a long insert, so you need another two meters' clearance above (plus a small winch). A dil fridge is limited in theory to something like 7 millikelvin, and in practice to higher values depending on model. They can typically extract only a few hundred microwatts of heat from the device under test, which is limited to a few cubic centimeters. You're also going to need lots of clearance around the fridge, for operators, rack-mount equipment, and space to move equipment down the aisles. All this is by way of saying that you need quite a bit of space, power, and money for each setup. Let's call such a setup a "pod".
I'm considering the design of a quantum multicomputer, a set of quantum computing nodes interconnected via a quantum network. Let's start with one node per pod, and again set our target at a machine for factoring a 1,024-bit number. If we put, say, five application-level qubits per node, and add two levels of Steane [[7,1,3]] code, we've got 250 physical qubits per node, and 1,024 nodes in 1,024 pods. If each pod requires an area three meters square, we need an area about 100 meters by 100 meters for our total machine (bigger than a football field, smaller than a football stadium).
The thermal engineering is a serious problem. The electronics for each qubit currently fill a 19-inch rack, but a lot of that is measurement, not control, and of course in a production-engineered system we can increase the integration. It's still going to be a lot of equipmentfor 250 qubits, and worse, a lot more heat. It seems unlikely that our thermal budget will allow us to put the control electronics in the dil fridge (and some of it may not operate properly at such low temperatures, anyway). So, we're going to have to control it from outside. That means lots of signal lines - one per qubit for control, plus quite a few more (maybe as many as one per qubit) for measurement and various other things. Probably 4-500 microcoaxes that have to reach inside the fridge, each one carrying heat with it. Yow. Unless you substantially raise the extraction rate of the dil fridge, each line and measurement device is limited to about a microwatt - plus the heat that will leak through the fridge body itself. In the end it's almost certainly a multi-stage system, with parts running at room temperature, parts at liquid helium temps, and only the minimum necessary in the dil fridge itself.
Finally, we have to think about money again. We've just set a limit of about $100K per pod. I've never priced dil fridges, but I'd be surprised if they're cheaper than that (I wonder what kind of volume discount you get when you offer to buy a thousand dil fridges...), and we have a bunch of electronics and whatnot to pay for, in addition to the quantum computing device itself! We can do better on floor space and money if we can fit more than one node per pod, but doubling or quadrupling the number of coaxes and the heat budget is a daunting proposition on an already extremely aggressive engineering challenge.
It's not that I think this linear extrapolation from our current state is necessarily the way production systems will really be built (it's also worth noting that NMR, ion trap, optical lattice, and atom chip systems would require a completely different analysis). I'm trying to create a rough idea of the constraints we face and the problems that must be solved. One thing's for sure, though: when I found my quantum computing startup, world-class thermal and packaging engineers will be just as high on my shopping list as the actual quantum physicists.