April 14th was World Quantum day and the most noticeable thing that happened was that Google presented us with a nice doodle. Should you get excited?

I understand the math of quantum physics and have taken university courses in quantum computation and I can tell you now I am deeply unimpressed by the prospect of quantum computing. This is not a moment like the emergence of ChatGPT, even if it is important. The reason it is important is not that it heralds the introduction of a new super computer and much of the hype surrounding the effort to build a quantum computer is very much misplaced.

The first thing to say is that Google's doodle, nice though it is, does nothing to help you understand quantum anything. Despite all of the many analogies designed to help the non-specialist have some idea of how QM works, nothing but being able to calculate is sufficient.

Back in the day when QM was new it was clear that no one understood it - how can the basic entity of matter have particle- and wave-like properties. No simple physical model is anywhere near correct because we have no experience of the world at the quantum level and trying to understand it with pictures of the macro world are doomed to failure. It's like trying to describe color to a being who sees only black and white. We simply don't have the physical experience to provide a model. This is the reason that physicists resorted to the motto "shut up and calculate". We may not have the experiences to model the fundamental entities of the universe, but the math works. It is a testament to the effectiveness of mathematics that it can take us places that our perceptions cannot - multidimensional spaces and the quantum world being two obvious cases. We reason by analogy but in the case of quantum mechanics the analogy is Hilbert spaces and eigenstates which are not generally considered to be physical analogies.

So what does this have to do with quantum computing?

The problem is that we tend to think of a quantum computer as if it was a digital computer, but with qbits rather than bits and from here we have the nonsense that a qbit can be all values at the same time. This isn't why quantum computers are important. A quantum computer is a sort of analog computer that works at the quantum level.

Analog computers have a talent for doing things quickly, but with a margin of error. For example, suppose you want to find the largest of a large set of numbers. Typically this takes O(n), but you could build an analog computer to do the job. Just take lengths of wood, each one cut to the length of a number, and then just stack them all end up on a flat surface; the maximum is the tallest one you can see sticking out of the pack. OK, this is a weak practical example, but it does illustrate the problems of analog computing. How accurate the answer is depends on how accurately you cut the lengths and how accurately you can spot the tallest in the pack.

Quantum computing is a lot like this.

In the case of quantum computing you have to find quantum states that represent the physical states - usually a superposition of qbits. Then you make some sort of measurement that forces the qbits into a pure eigenstate and you hope that this is the solution to your problem.

It is difficult to find an easy-to-understand example, but consider the Fourier transform that splits a signal into its frequency components. Classically this is done by multiplying values in a complex way that takes at least nlogn. A quantum Fourier transform is just a matter of setting up a quantum state and then applying the qbits to set of quantum gates. Of course, it takes time to construct the quantum gates and the gates have to be used more than once. A quantum Fourier transform can be computed in constant time assuming we have the quantum gates ready to be used. This is a bit like assuming we have the pieces of wood already cut to the right lengths. 

The quantum Fourier transform is key to the all-important Shor factoring algorithm, which is the real motivation for investing so much in quantum computing. With a big enough quantum computer running the Shor algorithm, we can factor numbers into primes and hence crack codes.

So what can a quantum computer be used for apart from cracking codes?

We can simulate quantum systems and this is what Google offers as the motivation for working on such machines. A recent blog post outlines 3 real-world problems that can be solved - better medicine, better batteries and new energy resources. These really are quantum computation as simulation. I'm underwhelmed by the examples and not at all convinced that they lead to significant breakthroughs.

I have yet to encounter an algorithm of the same abstraction as Shor's or Grover's algorithms - most are much more clearly simulations of the quantum world rather than quantum manipulations that model something abstract like factoring or searching.

Has anyone thought of asking a LLM to work out a better drug, battery or energy resource? Come to that what about asking how to factor numbers?

Perhaps AI is all we need.

More Information

Celebrate World Quantum Day with this mesmerizing Doodle

3 real-world problems that quantum computers could help solve

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