Quantum computing can be chaotic, but key properties of that chaos may actually help us develop useful devices. That is the finding of a study of the behaviour of quantum bits, or qubits, which has shown that their chaotic nature may be easier to predict than thought.

Quantum computers use qubits as the basic unit of memory, the same way regular computers use bits. The difference is that while a bit can only be in one of two states – a 1 or a 0 – a qubit can be in a combination of the two. When qubits are put into groups, such as on a quantum computer chip, they can display chaotic behaviour, each oscillating between different values. That can make changes in their final states hard to predict.

Alexandre Zagoskin at Loughborough University in the UK and his colleagues simulated this chaotic behaviour for certain types of quantum computing systems. They found that systems of five or more qubits display not just chaos, but hyperchaos, which makes their behaviour even more unpredictable.

“Chaos appears when a small difference in initial conditions causes a very fast-growing difference in the trajectory of the system’s behaviour,” says Zagoskin. “In hyperchaos, the trajectories run away from one another in many directions.”

However, the chaotic dynamics of the system can be reined in by changing the properties of the energy entering the system. That could make hyperchaos useful as a random number generator, one of the potential early uses of quantum computers.

More importantly, though, the researchers found that adding more qubits didn’t make the hyperchaos in the system grow exponentially as they had suspected it would. Instead, it grew linearly – each additional qubit added one more layer of chaos. The system is much easier to describe mathematically than it would be if adding qubits made the chaotic behaviour skyrocket.

“This system shows very non-trivial and new quantum phenomena which we have never seen before,” says Shiro Kawabata at Japan’s National Institute of Advanced Industrial Science and Technology. “In this sense, this system can be regarded as a new type of quantum simulator, a ‘chaotic quantum simulator’.”

Simulating quantum behaviour with classical computers is a challenge. If simulating lots of qubits precisely with a classical computer were possible, there would be no need for quantum computers.

“We can calculate how a small group of qubits will behave, but we cannot extract from this information about how a realistic large group of qubits will behave,” says Zagoskin. “This is a bottleneck in quantum computing.”

This work won’t help us simulate the specifics of a large group of qubits, Zagoskin says, but it may help in figuring out their general behaviours, such as how to control a system to minimise chaos. He likens it to building a model aeroplane in the process of engineering a real one: it won’t behave exactly the same as if it were life-sized, but it can nevertheless help guide the final design.

Martin Weides at the University of Glasgow in the UK says that understanding how and when hyperchaos arises “will be extremely valuable for the design of future large-scale quantum simulators and computers”. The researchers have already started the next step in this – to test the theoretical work in actual quantum computers.

Journal reference: npj Quantum Information, DOI: 10.1038/s41534-020-00339-1