Hyperchaos possibilities for modelling complex quantum systems

Tuesday, 26 January 2021

Physicists have discovered a potentially game changing feature of quantum bit behaviour which would allow scientists to simulate complex quantum systems without the need for enormous computing power.

For some time, the development of the next generation of quantum computer has limited by the processing speed of conventional CPUs.

Even the world’s fastest supercomputers have not been powerful enough, and existing quantum computers are still too small, to be able to model moderate-sized quantum structures, such as quantum processors.

However, a team of researchers from the University of Nottingham's School of Physics & Astronomy and Loughborough and Innopolis universities have now found a way to bypass the need for such massive amounts of power by harnessing the chaotic behaviour of qubits - the smallest unit of digital information.

When modelling the behaviour of quantum bits (qubits) they found that when an external energy source, such as a laser or microwave signal, was used the system became more chaotic – eventually demonstrating the phenomenon known as hyperchaos.

When the qubits were excited by the power source they switched states, like regular computer bits which shift between 0 and 1, but in a much more irregular and unpredictable way.

However, the researchers found that the degree of complexity (hyperchaos) did not increase exponentially as the size of the system grew – which is what one would expect – but instead, it remained proportional to the number of units.

In a new paper, Emergence and control of complex behaviors in driven systems of interacting qubits with dissipation, published in the Nature journal NPJ Quantum Information, the team show how this phenomenon has great potential for allowing scientists to simulate large quantum systems.

Dr Weibin Li, from the School of Physics and Astronomy at the University of Nottingham said: “The results in this work are insightful for understanding complex quantum dynamics. Future quantum computers consist of thousands of quantum bits (qubits), which will be orders of magnitude more powerful than the fastest classical computer on the market. Here a full control and characterisation of the quantum computer is the key to perform correct and massive computing.

“In quantum realm, the number of degrees of freedom of a system grows exponentially with its size. As a full scale quantum computing on a true quantum computer is not available yet, the bottleneck is that only small-scale quantum computers, up to dozens of qubits, can be simulated using classical supercomputers."

Dr Alexandre Zagoskin, of Loughborough’s School of Science, said: “A good analogy is aircraft design.In order to design an aircraft, it is necessary to solve certain equations of hydro(aero)dynamics, which are very hard to solve and only became possible way after WWII, when powerful computers appeared.Nevertheless, people had been designing and flying aircraft long before that.

“It was because the behaviour of the airflow could be characterized by a limited number of parameters, such as the Reynolds number and the Mach number, which could be determined from small scale model experiments.Without this, direct simulation of a quantum system in all detail, using a classical computer, becomes impossible once it contains more than a few thousand qubits.

“Essentially, there is not enough matter in the Universe to build a classical computer capable of dealing with the problem.If we can characterize different regimes of a 10,000-qubit quantum computer by just 10,000 such parameters instead of 2^(10000) – which is approximately 2 times a 1 with three thousand zeros – that would be a real breakthrough.”

The new results show that a quantum system shows qualitatively different patterns of general case behaviour, and the transitions between them are governed by a relatively small number of parameters.

If this holds generally, then the researchers will be able to determine the critical values of these parameters from, e.g., building and testing scale models, and, by taking a few measurements of the actual system, to tell whether the parameters of our quantum processor allow it to work properly or not.

As a bonus, the controllable complexity in the behaviour of large quantum systems opens new possibilities in the development of novel quantum cryptography tools.

Story credits

More information on the research is available from Professor Weiben Li at the University of Nottingham on or 0115 748 6751 or Jane Icke Media Relations Manager for the Faculty of Science at the University of Nottingham, on 0115 951 5751 or

Jane Icke - Media Relations Manager Science
Phone: 0115 7486462

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