The problem it is actually for

A chemist with a molecule she cannot compute

Nitrogen makes up most of the air. Plants cannot use it from the air, so almost every crop on earth depends on ammonia made in a factory. That factory runs at about 400°C and 200 atmospheres of pressure, and burns through roughly one per cent of the world’s energy supply doing it.

A bacterium in the soil does the same reaction at room temperature, using an enzyme called nitrogenase. Nobody can say exactly how. The active part of that enzyme is a cluster of iron and sulphur atoms, and to predict how its electrons arrange themselves you have to track them all at once — because in a quantum system, the parts are not separable.

That is the shape of the problem. Not “a very big sum”. A sum whose size doubles every time you add one more particle.

Why doubling is the whole story

Describe one electron’s state and you need a couple of numbers. Two electrons need four. Three need eight. The pattern is 2 to the power of n — one number for every combination the system could be in, and they all matter at once, because they can add and cancel against each other.

Work it through with real memory. A single one of those numbers takes about 16 bytes to store properly.

• 20 particles: 16 megabytes. A photograph.
• 30 particles: 17 gigabytes. A laptop, straining.
• 40 particles: 17 terabytes. A server room.
• 50 particles: 18 petabytes. More than the largest supercomputers hold.

Every extra particle doubles it. Not “makes it harder” — doubles it. There is no faster chip that fixes this, because the difficulty is not in the arithmetic. It is in how much there is to write down.

Meanwhile the bacterium in the soil does it in a fraction of a second, and it is not doing arithmetic at all. It is simply being a quantum system.

Feynman’s move

In 1981 the physicist Richard Feynman put the obvious question. If a quantum system is impossibly expensive to simulate on an ordinary computer, but nature runs it for free, why not build a computer that is itself quantum? Let the machine’s own particles do what the particles you are studying do.

That is what a quantum computer is. Not a faster computer. A machine built out of the same stuff as the problem, so that the problem’s difficulty stops being a difficulty.

This is why the honest list of things quantum computers are good for is short and specific:

• Simulating quantum systems — molecules, materials, chemical reactions. The original purpose, and still the strongest one.
• Problems with a hidden repeating structure. Factoring a large number is the famous one. It is not that the machine tries every factor; it is that the question can be turned into “what is the period of this pattern?”, and finding a period is something a quantum machine can do in one go.
• Some searching and optimisation, with a real but modest gain — roughly a square root, so a search taking a million steps takes a thousand. Useful. Not a revolution.

And the list of what it cannot help

This half matters more, because it is where the claims go wrong.

Anything whose difficulty is the amount of data is a bad fit. To work on a billion customer records, a quantum machine must first have those billion records loaded into it, one at a time. The loading takes as long as the ordinary computer would have taken to just do the job. The speed-up drowns before it starts.

So: not spreadsheets. Not video. Not databases. Not sorting. Not adding numbers faster. And not, in any general sense, the everyday work of the computer you are reading this on.

A quantum computer is a special-purpose instrument, like a wind tunnel. A wind tunnel is magnificent and it will not help you write a letter. Nobody is embarrassed by that, because nobody ever claimed a wind tunnel was the future of letters.

The instrument and the world

There is a habit of thought worth breaking here. We ask “how powerful is it?” as if power were one quantity, and machines could be ranked on it. That question has no answer. The useful question is narrower and harder: what shape is this problem, and does the machine share that shape?

The bacterium is not powerful. It is well matched. Most of what looks like capability, in machines and in institutions alike, is really a match between the shape of a tool and the shape of a job — and most disappointment is what happens when someone forgets to check.