There are multiple ways of building a qubit: Superconducting (transmons), NV-centers/spin-qubits, topological qubits, etc.

The superconducting qubits are the most well-known qubits and are also the easiest to build. The machines by IBM and Google, for instance, use superconducting qubits.

Spin qubits have sizes in the order of a few nanometers and thus have great scaling capabilities. The problem with superconducting qubits, on the other hand, is the size. Apparently, it is hard to shrink the size of a superconducting qubit (typically ~0.1mm).

What is the limiting factor in the size of superconducting qubits and why can this limiting factor not be scaled down?

Getting enough capacitance and maintaining coherence essentially set the size limit. A superconducting qubit, for the purposes of answering this question, can be imagined as an oscillator consisting of an inductor and a capacitor. The frequency of the oscillator can't be too high otherwise controlling the qubit becomes difficult. At Google, we typically work with the frequency range 4-8 GHz. A wide range of microwave generation, manipulation, and analysis tools are available off-the-shelf for this range.

The capacitor is built in a simple manner to reduce noise. Essentially a plus-shaped cut in a piece of metal. The kinds of techniques used to achieve large capacitors in small sizes such as a pair of meshed combs or some kind of multi-layer metal-dielectric sandwich increase field strengths and therefore the strength of interaction with imperfections in the chip, increasing noise. To get a large capacitance with this simple design requires significant space. Indeed, our qubits are closer to 1 mm center to center.

That's the answer to your question, but there's a premise in the set up of your question that big is bad. In my opinion, small is bad, and big is far more scalable.

We drive our qubits with microwaves, these are typically delivered with coaxial cables of diameter currently of order 1/32nd of an inch. If you imagine a million qubit computer, at our scale this is about a square meter, and getting a few million lines in sounds very achievable. I'm not sure why you would want a quantum supercomputer to be smaller than this.

I wanted to add a comment on Austin Flowers but it says I need 50 point reputations.

So essentially you need a low enough frequency in your superconducting circuit (4-8 GHz is Google's choice, to make use of established microwave spectroscopy tools). To get a low frequency, you need a high capacitance. To get a high capacitance, you need either:

  1. a large-size capacitor (1 mm from center to center at Google), or
  2. exotic technology such as a pair of meshed combs, but this will amplify decoherence.

So making smaller qubits is limited by (in some hierarchical way):

  1. the lack of cheap tools for working in a higher frequency region (above 8 GHz)
  2. the inability to get to low enough frequencies without using larger capacitance (could this be mitigated by adjusting the properties of the inductor? I don't know)
  3. the inability to get large capacitance without making the capacitor large [or] the inability to get large capacitance in small capacitors without increasing the noise.

A simple way to put it is that they are limited by decoherence/noise, but there's other ways to improve the design which might make it possible to make qubits smaller without increasing the noise too much.

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I have one final comment on the answer of Austin Fowler, which questions the validity of the original quesiton by saying that a few millions qubits can fit in a few square metres, so why do you want any smaller than that? That is an interesting point. In classical computing we keep thinking about wanting to make them smaller so that more gigs of RAM and more gigs of storage space can fit in our pocket or take up less space on the table, but quantum computers at present would only be "supercomputers" as Austin Fowler correctly pointed out. A few square meters isn't bad for a supercomputer.

However, it's not clear whether or not a few million qubits will be enough to do any useful, valuable, real-world computation, as Austin's series of Shor algorithm papers suggest (with error correction, which will definitely be needed to do anything useful, you will need billions of qubits). It is true that 100 qubits can't easily be simulated, in general, on a classical computer (people once said 25 qubits, then 30 qubits, then Haner & Steiger did 45 qubits with 500TB of RAM, then Sergio Boixo said 47 qubits in a 7x7 array, then IBM and Chinese groups simulated 60, then 70, on classical supercomputers, so let's just say 100 qubits for now). Simulating a fully controllable 100-qubit system will be interesting to study the physics of the system itself, and may provide insight into how to better engineer better quantum computers in the future, but "simulating quantum computers" is a very very tiny portion of what the world uses supercomputers for (and in this case one can argue that building quantum computers doesn't even help, since we're talking about simulating a quantum computer with a classical computer in the first place).

Most real-world HPC problems: weather modeling, stock market prediction, image processing for satellite data, astrophysics, etc. are not going to be solved with a few million qubits physical qubits error correcting a thousand logical qubits. If we need a billion qubits to outperform a classical computer on a real-world problem (I think we might need even more), then your square meter becomes 1000 square meters which is 0.1 hectares. 10 billion qubits would take up all the grass within a 400m running track, and this is then going to be too much effort to control with microwaves, to maintain in decent condition, and to power. ORNL's Titan is 400 square meters. If the quantum computer is allowed to be 1000 square meters (for 1 billion qubits), then let's allow the classical computer to be that big. Then if 1 billion was big enough to beat Titan, maybe you'll need 2 billion to beat Titan's bigger brother.

Hopefully there will be a cross-over point at some point, but I agree both with Austin (that we reached the point where there's many more important things to think about than just the size of the qubits) and with Nippons, who asked this question, because it does seem that we can use some size reduction for the qubits.

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