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quantum-inspired optimisation methods that use annealing on classical hardware today and we use it to solve customer problems better than in the past. So there is something we can do on classical hardware.

How can you identify which applications are suitable for quantum computing? What are the problems that I can solve much better using quantum hardware in the future? When looking at that, we see not just which problems we can solve quantumly, but which problems can be solved better and faster than on any potential classical machine. We found there are three conditions we

10,000? Will it run for an hour, a week, a month or a year? If it’s a year, we will need to think about how to reduce the run times. Intermediate-scale quantum systems can be used to experience quantum computing, so users can learn how to run something on quantum hardware and see how it works. Finally, we have quantum solutions. What

we found here is that, as we think about how we will use quantum hardware in the future, and as we develop the new quantum algorithms, we realise that we can actually run that algorithm in a variant of classical hardware. And so we’re making progress with

classical solutions on classical hardware by thinking ‘quantumly’. Quantum brings a disruptive mindset to solve problems differently. And we use that to invent better algorithms, which we can deploy already today in Azure, on classical hardware.

If a problem is seemingly intractable, how can a scientist think about how to solve it?

I am tackling problems that are seemingly intractable, but where I have an idea of how a quantum computer could solve it. To solve it on quantum hardware, I think about a different approach, because I want to use the power of the quantum computer. I formulate the problem in a different way, so that I can then apply a certain quantum

20 Scientific Computing World Summer 2021

algorithm, which I know will have to speed up on future quantum hardware. And as I do that, and as I reformulate the problem to fit the acceleration offered by the quantum computer, I then sometimes realise this new viewpoint, this new way of attacking the problem. It gives me new ideas – how it can be solved classically. Sometimes, we have seen this can be thousands of times faster than the typical way it was done classically. And so instead of intractable in this case, I say these are seemingly intractable problems where we didn’t see a way of doing it classically. But we saw a way of maybe doing it using quantum, and then, by working out the details, we find a new way of solving the problem – potentially very fast – on classical hardware. If I think I can solve it classically, then I

don’t even think about it. But as quantum opens the possibility to take a new look, then I realise, maybe I was wrong, there is a better way of tackling the problems classically. And that gets triggered by quantum thinking, by just the possibilities that quantum will offer. And then, of course, once we have quantum hardware, the solution will work even better and faster in those cases. In one case, where we were looking into quantum annealing, we realised you could implement quantum annealing efficiently on classical hardware. We have plenty of

need for that. First, we need a problem where there is a quantum algorithm with quantum speedup. Secondly, we need a problem that acts on small data, not big data – the reason is your quantum computers have a slower clock speed than classical ones, and so I/O will be a bigger challenge than with classical computing. Thirdly, again, because the clock speed is slower, and because qubits are much more complex than transistors, every operation will take longer, and so the classical hardware has a big constant advantage over the quantum hardware. But it can overcome that by the quantum algorithm having to do far fewer operations. What we need for that are quantum algorithms with exponential quantum speedup, so that I can beat the constant advantage that the most simple classical system has.

What are the main applications being targeted for quantum computing today? The main applications in the mid-term will be for those such as chemistry and material science, where you can predictively calculate the properties of materials, molecules, catalysts and chemicals. When you look at what is needed to do that, for the size of a problem they can’t do classically, then you see we need about 1 million qubits. That means you have to scale the noise,

the physical qubits, to the size of a million – and more. So we need technology where we get a qubit that is scalable to millions – and that’s fast. But we need more than the qubit. We need also to control a million qubits to operate them, using a software stack and control stack. And so we work on the whole stack, to cryogenically control the qubits, the software stack, the algorithms, the applications and the cloud services.

What are the biggest challenges that still face quantum development? I think the biggest challenge, ultimately,

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