The life of a qubit can be stressful. To keep information moving within a quantum computer, qubits need to endure freezing temperatures of near absolute zero (roughly -460 Fahrenheit) and tune out distractions all around them like stray magnetic and electric fields or “cross-talk” from their neighbors.
These annoyances can create errors in quantum systems and make it impossible for qubits to hold on to information flowing through them. Devising ways to eliminate these errors is one of quantum computing’s biggest open questions. Now, a team of physicists have discovered a new way to ignore these errors using a high-school mathematics lesson and 2-D time—that is to say, time that exists in two dimensions.
This mind-bending discovery is detailed in a new paper published on Wednesday in the journal Nature. Co-author Andrew Potter—an assistant professor of physics at the University of British Columbia—told Motherboard in an email that while this work deals with new phases of matter, it is still different in many ways from the solid, liquid, gas phases we typically think of.
“The modern way of thinking about phases of matter is to define a phase as a region of parameter space where you can move around without encountering a phase transition,” Potter explained. “For example, a solid doesn't immediately melt into a liquid if you warm it up, only if you heat it up past a critical temperature, its melting point.”
Instead of looking at how temperature can transform matter, Potter and colleagues instead focused on how time could maintain boundaries around a phase to create something called a “dynamic topological phase.” In this case, instead of temperature driving phase changes, errors in a quantum system do.
By keeping their system in this phase, the team showed that they were able to protect qubits from one class of errors that threaten to disrupt them, Potter said. However, to actually maintain this state these qubits need something that sounds impossible: two-dimensional time.
To pull this off, the team turned to a historic and prolific pattern in mathematics called the Fibonacci sequence. First codified in the 1100s by an Italian mathematician, the Fibonacci sequence describes a sequence of numbers in which each number is the sum of the two the come before it and has often been connected to forms of mathematical beauty in nature, for example in the spiral of a sunflower’s seeds.
For the purposes of their work, Potter and colleagues were more interested in the ratio between these numbers and how it could help them direct lasers at trapped qubits.
“The Fibonacci sequence is a non-repeating but also not totally random sequence, which effectively lets us realize two independent time-dimensions in the system,” Potter said.
Essentially, the nature of the Fibonacci sequence created a quasi-periodic rhythm that shares similarities with another strange type of physics called a quasicrystal. Where a typical crystal will have both ordered and repeating structure (like a honeycomb), a quasicrystal will have order but not repetition. This is because a quasicrystal is actually a flattened 1- or 2-dimensional representation of a higher dimensional form.
The same way that quasicrystals hide extra dimensions, a quasi-periodic sequence like Fibonacci’s can conceal an extra dimension in time, the team determined.
“This effectively lets us squash two time-dimensions into a single time direction so that we can fully-dynamically protect the edge qubits,” Potter said.
The team tested this out on trapped qubits in a quantum computer and found that these laser pulses were able to keep the qubits stable for the length of the experiment (about 5.5 seconds) compared to 1.5 seconds for simple periodic laser pulses.
While this work is far from eliminating all quantum errors, it is early evidence that such an approach could help improve quantum memory and computing in the future, Potter said.
“It shows that, at least in principle, there are ways to manipulate and control quantum systems that are largely insensitive to mistakes and an important class of errors, which I'm optimistic could be useful in the long run,” he said.