*Interest in quantum computers is taking off as governments and big business look for ways to gain a competitive edge through cutting edge technology.*

*In this three-part series, Information Age looks at how quantum computers work, their applications, and the continued role Australian scientists and engineers play in the technology's development.*

In part one of this series on quantum computing we tried to understand what quantum computers are, how they work, and what they do differently to classical computers.

This week we will look at the uses of quantum computers and why they are so sought after.

Keep in mind that quantum computers are fundamentally different to classical computers, in large part because of their probabilistic nature.

Quantum computers don’t offer a mere speed-up to classical systems.

Rather, they are a whole new realm of computing, the use of which is being worked out alongside the immense engineering challenges posed by building large-scale quantum computing systems.

According to Professor Michael Biercuk, CEO and founder of Q-CTRL, one of the biggest uncertainties in the field of quantum computing is around what types of problems can be solved.

“Shor’s Algorithm is actually a really interesting example,” he told *Information Age*. “It’s the algorithm that motivated the development of the entire field.”

In 1994, mathematician Peter Shor proposed an algorithm for efficiently finding the factors of a number. Factorisation of large prime numbers is a major part of modern cryptography precisely because it is a problem that classical computers find difficult in proportion to the size of the number.

Shor developed his factorisation algorithm to leverage the conceptual quantum computers that physicists like David Deutsch had been researching to factorise numbers in polynomial – as opposed to exponential – time.

“It was very exciting,” Biercuk said about Shor’s Algorithm. “The benefits were really large, but because of the area in which it has an impact, cryptography, the National Security Agency (NSA) in the US issued its first ever open university funding announcement.”

Since Shor’s Algorithm had the potential to crack open cryptography – a naturally valuable area for government spy agencies – it fuelled an arm’s race for quantum computing research.

There are concerns that quantum computers could be disastrous for cryptocurrencies like Bitcoin and already new methods of post-quantum cryptography are being developed as a way of protecting data that is stolen now from being decrypted by quantum computers in the future.

You may have noticed that RSA encryption hasn’t been broken yet, and that’s because implementing Shor’s Algorithm is “much harder than people thought”.

“It’s going to require a very big machine with a huge number of quantum bits and extraordinarily good performance,” Biercuk told *Information Age*.

“The likelihood that we would realise such a machine has kind of receded to the horizon.”

**What else?**

Shor’s Algorithm offers a theoretical look at the advantage quantum computers can have over their classical counterparts, but it’s not very useful now or, potentially, for years to come.

So what other uses are there for quantum computers?

An obvious one is in quantum simulations which are particularly useful for chemistry.

The underlying mathematics of quantum systems is incredibly information-rich.

As a demonstration of this, physicist Robert Hartree noted back in the 1930s that if all the wave functions for the electrons of a single iron atom were tabulated, it would take 10^{78} table entries – more numbers than there are atoms in the solar system.

Iron, it turns out, is extremely useful in biochemistry, especially in the FeMoco molecule which is important for nitrogen fixation through the hundred-year-old Haber process that gives us fertiliser.

Dominic Berry is an Associate Professor at Macquarie University whose expertise is in quantum information.

He says accurate simulations of FeMoco could lead to a more energy efficient, and cheaper, process of producing fertiliser.

“People have been looking at the same process from within biological systems, which is very efficient, but no one has been able to turn this into an industrial process,” he told *Information Age*.

“It's hoped that if there was better understanding of how this actually works biologically then you might be able to make some modification to it and use it in the industrial nitrogen fixing process.”

That’s just one example. Simulations of small chemical systems – which have natural quantum effects – could help with discovering new drugs and medical treatments or lead to engineering molecules that have desirable properties for advanced technologies.

The problem with simulating these quantum systems is that the amount of information they hold grows exponentially, like when a classical computer tries to factor large numbers.

“Chemists have been working on methods of simulating these things for a long time,” Associate Professor Berry said. “And they’ve been able to get around the problem of this exponential blow up with lighter atoms.”

Quantum algorithms allow for more accurate simulations of a quantum system’s total energy and how that evolves over time, a Hamiltonian, which can be represented as a matrix that is more directly transposed onto quantum computers.

“For some particular task you want to achieve in a quantum algorithm, you can try to encode it into a Hamiltonian and then run a phase estimation algorithm on top of that to work out the energy level of a system,” Associate Professor Berry said.

“These are individual things we can do with quantum computers that can be combined for these types of simulations.”

**Enter the matrix**

Quantum algorithms are currently being developed in parallel with the engineering efforts to build and scale-up quantum computers.

For people who work closely with industry, like physicist Casey Myers from the University of New South Wales, it’s not so much about trying to find a catch-all algorithm that could theoretically break cryptography as Peter Shor, but rather using the existing tool kit of quantum computers to solve specific problems.

“You have to be realistic when you look at some of these things,” he told *Information Age*.

“So if someone says that hard problem is the travelling salesman problem, that’s fully general and you have to manage expectations so they know going in that there's a good chance quantum won't help.

“But there are other types of problems where quantum will help and that’s the fun part of my job – trying to find and solve those problems.”

It comes down to using what quantum computers are naturally good at; things like producing randomness can be invaluable for Monte Carlo simulations that involve sampling random distributions of numbers; or the interaction of large matrices, as with Hamiltonians.

“Say the information in your problem can be put into a matrix,” Myers said. “Then based on that matrix you need to do certain things to that data to solve your problem – maybe inverting the matrix, or exponentiating the matrix, or finding the eigenvalues and eigenvectors of it.

“All of these things have provable speed-ups from quantum algorithms.”

Machine learning, as a field that involves manipulating large tables and matrices of data, is one such field that could see the value of quantum algorithms.

**Early adopters**

Government and industry bodies are very much looking into how they can tap into this emerging technology to gain an advantage, even if quantum advantage hasn’t yet been reached.

Professor Biercuk’s company Q-CTRL is working with Transport for NSW to use quantum computing as a means of solving network optimisation problems.

He said organisations and businesses getting involved with quantum computing all have one thing in common – a view of the long-term potential for this technology.

“These are organisations that have multidecadal business plans,” he told *Information Age*.

“Yes, they answer to the street on a quarterly basis but they plan for technology on 10-plus year time horizons.

“Across different sectors, what we see is that companies which know the relevance of strategic advantages, that tend to invest early to mitigate risk and get the first mover’s advantage – they’re the ones getting into the field now.”

If you recall part one of this series, you’ll know that Australia led the world in developing quantum computers at the start of the millennium.

We had the first mover’s advantage here on technology that has the potential to radically transform industries across the economy.

But there are concerns that Australia’s quantum advantage has been neglected through a lack of funding and support.

World-class researchers are heading overseas in search of greener pastures and we are at risk of becoming an also-ran in the race to quantum supremacy.

*In part three, we'll look at the state of the Australian quantum ecosystem and what the government can do to support it.*