This Beautiful Math Equation Could Herald a Breakthrough in Quantum Computing

At first glance, the Fibonacci sequence may seem like nothing more than a mathematical trickery. But look around, and it shows up again and again and again, in computing and in nature. It’s elegant logic: add the two previous elements to get the next one.

Now physicists have applied that logic to another setting: the inside of a quantum computer. Using a laser, they created a new phase of matter that changes state at a Fibonacci-like rate over time. The results, published in Nature June 20 marks the first time a phase quite like this has been created in the real world.

What’s new – This new phase was composed of ten ions of ytterbium, a rare earth element widely used in quantum computers, caged in an electric field.

Ions are only part of the story. The other is a laser that the scientists fired at the ions to manipulate them. The researchers were able to flip them, at a steady rate, between one of two states. Call them A and B.

What made this phase unique was the pattern it followed. Instead of a straight periodic pattern, the researchers added a second layer in the style of the Fibonacci sequence. So instead of an ABABAB pattern, they put the ions through something like A-AB-ABA-ABAAB-ABAABABA, each segment the sum of the previous two.

The Fibonacci sequence, sometimes called the golden ratio, appears repeatedly in nature. (This illustration does not represent nature.)Shutterstock

Over the past few years, the theoretical physicists behind the work had refined the theory of how this phase works. They had modeled and simulated it on their own (classic) computers. But there was no substitute for the real thing.

“The truth [quantum] computers are very complicated devices that have many sources of error that you don’t necessarily anticipate,” says Philipp Dumitrescu, theoretical physicist formerly at the Flatiron Institute in New York and lead author of the paper. Reverse.

So they turned to a quantum computer operated by Quantinuum (a spin-off of engineering conglomerate Honeywell), located in the Denver suburb of Broomfield, Colorado. Inside the cold core of this quantum computer, they made the phase work as intended.

Here’s the background — The qubit is the cornerstone of a quantum computer. A qubit is analogous to the bits that sit at the heart of normal or classic computers; they can be a “zero” or a “one”. But due to the quirks of quantum mechanics, a qubit can be a whole rainbow of combinations of these two states: what physicists call quantum superposition.

Quantum computers are unlikely to replace the world’s work machines and gaming platforms anytime soon. But some scientists believe they could be useful for cryptography and pharmaceutical discovery. Physicists have a much more personal use: by using qubits to simulate other computers, they can perform quantum experiments that aren’t really possible in any other context.

While almost all classical computers in existence use bits of silicon, quantum computers today use all sorts of different things like qubits. Some use photons. Some use electrons. Some use atomic nuclei. Some use small contraptions made from superconductors. Some, like the one in this experiment, use ytterbium ions. As long as something has two states in which a “zero” and a “one” occur respectively, and as long as that thing could be in a superposition of those two states, it could theoretically function as a qubit.

Quantum computers, like those at the Leibniz Computing Center (pictured), require their qubits to exist in a state of “superposition” – both 1 and 0 rather than one or the alliance/photo alliance/Getty Images

Why is it important – One of the major challenges in quantum computing is that qubits are tricky. They sit on a precarious precipice, liable to lose their information due to interference from all sorts of seemingly minute outside noise: interactions with other particles, even vibrations from heat (which is why most quantum computers have to be cooled to temperatures just above absolute zero. )

Physicists therefore seek to make qubits more resistant to chance. One way to do this is to place the qubits in a certain phase. “There are particular types of quantum matter phases that have ‘protected’ quantum information,” says Dumitrescu. “These phases of matter can undo all kinds of errors.”

This is precisely what this new phase of matter does. Continuous manipulation of qubits with a laser can strengthen qubits, making them stronger and more durable. Using not one but two patterns, thanks to the Fibonacci sequence, can give qubits an extra layer of protection. Until now, Dumitrescu, this had not been tried in a quantum computer.

The results of the researchers bear this out. Under a quasi-periodic laser, ytterbium ions at the edge of the qubit cluster lasted more than three times longer than the same ions in periodic pulses.

And after – This experiment brought together theoretical physicists with their experimental counterparts in quantum computing. For the former, it was a justification of their calculations.

But for quantum computer scientists, the work has only just begun. If they want to use this phase in their operations, they will have to create new algorithms and new routines that work with the new phase. And there may be other phases like this, which demonstrate quasi-periodicity, that they may want to play around with.

“There is still a lot of interesting work and research to be done,” says Dumitrescu.

Sherry J. Basler