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Soft matter and liquids

Soft matter and liquids

Topological defects in liquid crystals resemble quantum bits, say mathematicians

27 Aug 2022
Nematic liquid crystal
Defect bits: representation of two n-bits along a defect line (shown in black). Shown are the orientations of the rod-like molecules that comprise liquid crystals. (Courtesy: Žiga Kos and Jörn Dunkel/Science Advances)

Topological defects in liquid crystals are mathematically analogous to quantum bits, researchers in the US have shown theoretically. If a system based on this principle could be implemented in practice, many of the advantages of quantum computers could be realized in a classical circuit – avoiding the considerable challenges facing those trying to develop practical quantum computers.

Nematic liquid crystals are rod-shaped molecules that tend to line up with one another and whose alignment can be manipulated by electric fields. They are used in display systems that are found widely in mobile phones, watches and other electronic gadgets. Topological defects occur in nematic liquid crystals where the alignment changes. The similarity of these systems to the quantum world has been known for some time. In 1991, Pierre-Gilles de Gennes won the Nobel Prize for Physics for his realization that the physics of superconductors could also be applied to defects in liquid crystals.

Now, applied mathematicians Žiga Kos and Jörn Dunkel of Massachusetts Institute of Technology have looked at whether nematic liquid crystals could prove useful as a novel computing platform.

Higher dimensional state space

“We all know and use digital computers, and for a very long time know people have been talking about alternative strategies like liquid-based computers or quantum systems that have a higher dimensional state space so you can store more information,” says Dunkel. “But then there’s the question of how to access it and how to manipulate it.”

Google and IBM have produced quantum computers using superconducting quantum bits (qubits), which need cryogenic temperatures to prevent decoherence, whereas Honeywell and IonQ have used trapped ions, which require ultra-stable lasers to perform gate operations between ions in electrical traps. Both have made remarkable progress, and other protocols such as neutral atom qubits are at earlier stages of development. All of these, however, employ highly specialized, delicate protocols that are not implemented in liquid crystal systems.

In their new work, the researchers demonstrate that, although the physics are different, one can draw a mathematical analogy between the behaviour of a topological defect in a liquid crystal and the behaviour of a qubit. It is therefore theoretically possible to treat these “n-bits” (nematic bits), as the researchers have called them, as though they were qubits – and to use them to execute quantum computing algorithms, even though the actual physics governing their behaviour can be explained classically.

Beyond classical computing

Or at least, that’s the plan. The researchers demonstrated that single n-bits should behave exactly like single qubits, and therefore that single n-bit gates were theoretically equivalent to single qubit gates: “There are other gates in quantum computing that operate on multiple qubits,” explains Dunkel, “and these are needed for universal quantum computing. These are something we do not have at the moment for the liquid crystal gates.” Nevertheless, says Dunkel, “we can do things that go beyond classical computing.”

The researchers are continuing their theoretical work in the hope of gaining a better understanding of the mathematical mapping between multiple qubits and multiple n-bits to ascertain how close the analogy really is. They are also working with soft matter physicists who are attempting to create the gates in the laboratory. “We hope that will happen over the next one or two years,” says Dunkel.

Dunkel and Kos describe their study in a paper in Science Advances. Theoretical and computational physicist Daniel Beller of Johns Hopkins University in the US is cautiously impressed: “I really like this paper,” he says; “I think it’s potentially very significant.” He notes the claims that have been advanced for the abilities of quantum computers to run algorithms using far too many resources or much too long to make them feasible on a classical computer and says that “this work proposes that those concepts might be testable and those computational speedups achievable in a system that doesn’t depend on very cold temperatures or preventing quantum decoherence”.  He adds “it’s a great theoretical and computational demonstration that, because physics is at heart an experimental science, should next be checked by experiment.” He cautions, for example, that realizing some of the assumptions used in the model, such as that the defects stay still while the liquid crystal flows around them will require “some design considerations in the experiments”.

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