Physics

Melting time crystals could help us model complex networks like the human brain

Passing electricity through a piece of quartz crystal generates a pulse you can literally set your watch by. Set a time crystal melting, on the other hand, and it just might pulse with the deepest secrets of the Universe.

A team of researchers from institutions across Japan has shown the quantum underpinnings of particles arranged as a time crystal could in theory be used to represent some fairly complex networks, from the human brain to the internet, as it breaks down.

“In the classical world, this would be impossible as it would require a huge amount of computing resources,” says Marta Estarellas, a quantum computing engineer from the National Institute of Informatics (NII) in Tokyo.

“We are not only bringing a new method to represent and understand quantum processes, but also a different way to look at quantum computers.”

Ever since they were first theorised in 2012 by Nobel Laureate Frank Wilczek, time crystals have challenged the very fundamentals of physics.

His version of this novel state of matter sounds suspiciously like perpetual motion – particles rearranging periodically without consuming or shedding energy, repeating in patterns through time just as run-of-the-mill crystals do through space.

This is because the thermal energy shared by their constituent atoms can’t settle neatly into an equilibrium with their background.

It’s a little like having a hot cup of tea that remains a tiny bit hotter than room temperature no matter how long it’s been on your desk. Only, since the energy in these tick-tocking clumps of matter can’t be put to work elsewhere, time crystal theory safely avoids violating any physical laws.

Just a few years ago, experimental physicists successfully arranged a line of ytterbium ions in such a way that when struck with a laser, their entangled electron spins fell out of equilibrium in this very fashion.

Similar behaviours have been observed in other materials, providing novel insights into the way quantum interactions can evolve in systems of entangled particles.

Knowing time crystal-like behaviours exist is all well and good. The next question is whether we can harness their unique activity for anything practical.

In the new study, by using a set of tools found in graph theory to map potential changes in a time crystal’s arrangement (as seen in the clip below), researchers showed how a discrete unravelling of a time crystal’s arrangement – its melting, if you like – mimics a category of highly complex networks.

“This type of networks, far from being regular or random, contains nontrivial topological structures present in many biological, social, and technological systems,” the researchers write in their report.

Simulating such a highly complex system on a supercomputer could take impractically long periods and serious amounts of hardware and energy, and that’s if it could be achieved at all.

Quantum computing, however, relies on a completely different way to carry out computations – one that uses the mathematics of probability embedded in states of matter called ‘qubits’ prior to being measured.

The right combination of qubits arranged as time crystals swinging back and forth into oblivion could represent signals moving across vast webs of neurons, quantum relationships between molecules, or computers messaging one another around the globe.

“Using this method with several qubits, one could simulate a complex network the size of the entire worldwide internet,” says NII theoretical physicist Kae Nemoto.

Applying what we learn in time crystals to this emerging form of technology could give us a whole new way to map and model anything from new drugs to future communications.

As it is, we’re barely scratching the surface of the potential behind this new state of matter. Based on research like this, we can be confident time is on our side when it comes to the future of quantum computing.

This research was published in Science Advances.

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