Researchers created a large, complex, two-dimensional “time crystal” on an IBM Quantum Heron r2 chip, as described in a paper published today (Jan. 28) in Nature Communications.

This work from a team including Basque Quantum Initiative (BasQ), NIST, and IBM scientists showcases the dramatic progress of IBM quantum hardware, the power of today’s quantum computers to drive meaningful work in other scientific disciplines, and the possibilities that open up when quantum and classical hardware resources work together.

What is a time crystal?

Crystals are matter organised into repeating patterns that resist deformation. Diamonds are carbon atoms arranged in a tight crystalline structure of nested cubes. That structure is so resilient that construction workers use diamond cutters to slice through steel and concrete. Time crystals form their resilient patterns across time, rather than space.

“They’re an example of what we call ‘non-equilibrium dynamics,’” said Eric Switzer, a theoretical condensed matter physicist at the National Institute for Standards and Technology (NIST) and an author of the paper. “These are systems that don’t settle, but keep their repeating behaviour going.”

Pump energy into most matter, and it will dissipate into the environment. Pump energy into a time crystal and it will exhibit stable rhythms (usually of the spins of particles flipping back and forth). The system locks into a cycle, flipping back and forth in a pattern that typically lines up every other beat of the pump.

“Time crystals are a counterexample to the expectation that quantum information just gets scrambled,” said Niall Robertson, IBM research scientist and another author of the paper. “Even when we drive the system out of equilibrium, you still get a signature of the original quantum state… a stable, repeating pattern that shouldn’t survive once you add heat or look at large scales.”

How IBM hardware helped push time crystals to new scale and complexity

Nicolás Lorente is a researcher at the Center for Materials Physics in Donostia and part of BasQ. He conducted foundational research into time crystals before ever touching a quantum computer.

“We found when you put a chain of these atoms, iron or titanium for example, close together and align them, you can drive microwaves through them so they start flipping,” he said.

This early work focused on chains of atoms each one linked to the next in relatively simple structures. Signals would transmit linearly down the chain, and a single block in the middle of the chain could disrupt the whole crystal.

Today’s quantum computers, with large, error-mitigated, super-cooled processors isolated from the heat and noise of the universe, are (among other things) excellent sandboxes for studying quantum phenomena. Using Heron, the team constructed a 144-qubit, two-dimensional time crystal.

In two dimensions, signals move in much more complex ways through the many-body system.

“Dimensionality matters. It’s not the same thing to have things align in one dimension as in two. And size matters,” Lorente said.

Dynamics emerged that had never previously been studied in tabletop experiments or classical simulations.

“We absolutely needed the quantum system to be able to probe something as big as we did,” said Switzer.

This work helped to show that time crystals are robust beyond very small scales, which could have implications for future research.

“Up until now it wasn’t clear if this was possible outside very artificial models,” Robertson said. “Here we actually perturb it, go to a more realistic model in two dimensions, and still see the time crystal effect.”

This work advances our understanding of non-equilibrium systems, which could also have implications for understanding how information survives in more chaotic, open-ended quantum systems. There is some hope that time crystals could one day play a role in quantum computing, due to their ability to preserve information, or materials science.

Quantum and classical compute, working together

Whenever there is an interesting quantum result, one important task is verifying it.

“We know our community is skeptical,” Switzer said. “So we need a way to benchmark. We compare with classical simulations where we can, then use that to normalise the quantum results.”

The team used a state-of-the-art approach to simulate the quantum state on a tensor network using belief propagation, then compared the results to those from the quantum computer.

“Rather than seeing the classical method as a competing tool, the workflow lets it enhance the quantum results,” Robertson said.

As information came in from the classical hardware, the researchers were able to use it not only to confirm but to refine the quantum executions. That back-and-forth helped bring their time crystal into focus.

This is an early example of where we expect the most exciting quantum computing work to go soon: quantum and classical HPC resources feeding information back and forth in increasingly tight orchestration. As the loop gets tighter, we can begin to refer to quantum-classical architectures as “quantum-centric supercomputing.”

As we discussed in a recent blog(link), GPUs may supercharge such architectures. Capable of running many simple mathematical operations in parallel, they were well-suited to the work of sifting through tensors. Long term, many HPC executions will involve operations broken up between CPUs, GPUs, and QPUs, with each piece of hardware handling only the mathematics to which they are best suited.

What that means for time crystals remains to be seen. The next big step, the researchers said, will involve trying to build a more complex time crystal in the more interconnected environment of IBM Quantum Nighthark chips. On Nighthawk, qubits link to up to four neighbours, compared to up to three on Heron. The team is also interested to see what GPUs can do for the classical side of the work, Robertson said.

There are big open questions about the role of disorder in time crystals. Right now, researchers know some amount of disorder is necessary to stabilise a time crystal. But too much disorder threatens to shatter it.

“The question is, how much disorder can you get away with?” Switzer said.

As the computing advances, their work continues.

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