# What are quantum computers good for?

## Forget cracking crypto, think modelling reality itself to help build a better one

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### Applications of quantum computing

Why bother? Worldwide, a lot of research dollars are being poured into quantum computing, in spite of a widespread belief that it’s only application is to render today’s encryption algorithms useless.

What’s the point of spending research dollars on a theoretical construct of such limited application?

The idea that quantum computing is only good for large-number factoring is still widespread. But some of the standard tools of quantum computing are starting to chip away at this perception. Let’s look at two.

The Fourier Transform is one of the oldest: while the mathematics for representing a time-domain event in the frequency domain is well-understood, the more complex the wave you’re trying to analyse, the bigger the calculation. In certain settings a quantum computer is exponentially more efficient at performing Fourier Transforms than a classical computer.

This is very much a creature of the real world, spanning materials sciences, structural engineering, our understanding of waves, photonics, consumer electronics … the list goes on.

Another example is here: a quantum algorithm for solving linear equations (where you have a matrix and a known vector, and wish to compute an unknown vector). For some classes of linear equations, Harrow, Hassidim and Lloyd have demonstrated that a classical computer’s runtime will be exponentially greater than that of a quantum computer.

As we understand more about quantum algorithms, we’re learning more about the types of problems that quantum computers could be applied to. And as researcher Scott Aaronson describes in this blog post, it’s also becoming clear that one of the best applications for quantum computers is to help us simulate the quantum world. This post describes the limits of classical simulation, with the conjecture that even quantum computers based on linear optics are too complex to be simulated in a classical computer.

Simulating quantum systems is an application that today consumes a huge amount of the world’s supercomputer processor cycles – along with other big-science headliners like astrophysics, genetics, geoscience, materials science, meteorology, climate modelling and high-energy physics.

Why is so much effort expended on quantum simulation? Because that’s where the world begins. Quantum simulation helps us, for example, better understand what’s going on in the world of chemistry. That, in turn, leads to potential applications in materials science, genetics, and other disciplines.

In this *Nature* paper published last year, for example, European and Canadian researchers propose using quantum computers to (it sounds recursive) simulate the states available to … a quantum computer.

It’s neither silly nor trivial. As they explain in the abstract, the simulation is necessary so as to understand the equilibrium and static properties of the quantum system. But how many samples are needed for a researcher to be certain that they’ve fully characterized the quantum system – without making a “list of everything”?

Today, the problem is approached by sampling, using the Metropolis algorithm on a classical computer. The European/Canadian group propose an alteration to that algorithm that uses a quantum computer to obtain the samples.

If we can build them, quantum computers will help get the quantum universe to yield up more of its secrets – and the best way to prove we can build one is to build one! ®

*The Register* would like to acknowledge the generous assistance and collaboration of Associate Professor Michael Bremner of the Centre for Quantum Computation and Intelligent Systems at the University of Technology, Sydney, in preparing this article. All errors or omissions, however, are the author's.