When the ancient Incas wanted to archive tax and census records, they used a device made up of a number of strings called a quipu, which encoded the data in knots. Fast-forward several hundred years, and physicists are on their way to developing a far more sophisticated modern equivalent. Their “quipu” is a new phase of matter created within a quantum computer, their strings are atoms, and the knots are generated by patterns of laser pulses that effectively open up a second dimension of time.
This isn’t quite as incomprehensible as it first appears. The new phase is one of many within a family of so-called topological phases, which were first identified in the 1980s. These materials display order not on the basis of how their constituents are arranged—like the regular spacing of atoms in a crystal—but on their dynamic motions and interactions. Creating a new topological phase—that is, a new “phase of matter”—is as simple as applying novel combinations of electromagnetic fields and laser pulses to bring order or “symmetry” to the motions and states of a substance’s atoms. Such symmetries can exist in time rather than space, for example in induced repetitive motions. Time symmetries can be difficult to see directly but can be revealed mathematically by imagining the real-world material as a lower-dimensional projection from a hypothetical higher-dimensional space, similar to how a two-dimensional hologram is a lower-dimensional projection of a three-dimensional object. In the case of this newly created phase, which manifests in a strand of ions (electrically charged atoms), its symmetries can be discerned by considering it as a material that exists in higher-dimensional reality with two time dimensions.
“It is very exciting to see this unusual phase of matter realized in an actual experiment, especially because the mathematical description is based on a theoretical ‘extra’ time dimension,” says team member Philipp Dumitrescu, who was at the Flatiron Institute in New York City when the experiments were carried out. A paper describing the work was published in Nature on July 20.
Opening a portal to an extra time dimension—even just a theoretical one—sounds thrilling, but it was not the physicists’ original plan. “We were very much motivated to see what new types of phases could be created,” says study co-author Andrew Potter, a quantum physicist at the University of British Columbia. Only after envisioning their proposed new phase did the team members realize it could help protect data being processed in quantum computers from errors.
Standard classical computers encode information as strings of bits—0’s or 1’s—while the predicted power of quantum computers derives from the ability of quantum bits, or qubits, to store values of either 0 or 1, or both simultaneously (think Schrödinger’s cat, which can be both dead and alive). Most quantum computers encode information in the state of each qubit, for instance in an internal quantum property of a particle called spin, which can point up or down, corresponding to a 0 or 1, or both at the same time. But any noise—a stray magnetic field, say—could wreak havoc on a carefully prepared system by flipping spins willy-nilly and even destroying quantum effects entirely, thereby halting calculations.
Potter likens this vulnerability to conveying a message using pieces of string, with each string arranged in the shape of an individual letter and laid out on the floor. “You could read it fine until a small breeze comes along and blows a letter away,” he says. To create the more error-proof quantum material, Potter’s team looked to topological phases. In a quantum computer that exploits topology, information is not encoded locally in the state of each qubit but is woven across the material globally. “It’s like a knot that’s hard to undo—like quipu,” the Incas’ mechanism for storing census and other data, Potter says.
“Topological phases are intriguing because they offer a way to protect against errors that’s built into the material,” adds study co-author Justin Bohnet, a quantum physicist at the company Quantinuum in Broomfield, Colo., where the experiments were carried out. “This is different to traditional error-correcting protocols, where you are constantly doing measurements on a small piece of the system to check if errors are there and then going in and correcting them.”
Quantinuum’s H1 quantum processor is made up of a strand of 10 qubits—10 ytterbium ions—in a vacuum chamber, with lasers tightly controlling their positions and states. Such an “ion trap” is a standard technique used by physicists to manipulate ions. In their first attempt to create a topological phase that would be stable against errors, Potter, Dumitrescu and their colleagues sought to imbue the processor with a simple time symmetry by imparting periodic kicks to the ions—all lined up in one dimension—with regularly repeating laser pulses. “Our back-of-the-envelope calculations suggested this would protect [the quantum processor] from errors,” Potter says. This is similar to how a steady drumbeat can keep multiple dancers in rhythm.
To see if they were right, the researchers ran the program multiple times on Quantinuum’s processor and checked each time to see if the resulting quantum state of all the qubits matched their theoretical predictions. “It didn’t work at all,” Potter says with a laugh. “Totally incomprehensible stuff was coming out.” Each time, accumulating errors in the system degraded its performance within 1.5 seconds. The team soon realized that it was not enough to just add one time symmetry. In fact, rather than preventing the qubits from being affected by outside knocks and noise, the periodic laser pulses were amplifying tiny hiccups in the system, making small disruptions even worse, Potter explains.
So he and his colleagues went back to the drawing board until, at last, they struck upon an insight: if they could concoct a pattern of pulses that was somehow itself ordered (rather than random) yet did not repeat in a regular manner, they might create a more resilient topological phase. They calculated that such a “quasi-periodic” pattern could potentially induce multiple symmetries in the processor’s ytterbium qubits while avoiding the unwanted amplifications. The pattern they chose was the mathematically well-studied Fibonacci sequence, in which the next number in the sequence is the sum of the previous two. (So where a regular periodic laser pulse sequence might alternate between two frequencies from two lasers as A, B, A, B…, a pulsing Fibonacci sequence would run as A, AB, ABA, ABAAB, ABAABABA….)
Although these patterns actually emerged from a rather complex arrangement of two collections of varying laser pulses, the system, according to Potter, can be simply considered as “two lasers pulsing with two different frequencies” that ensure the pulses never temporally overlap. For the purpose of its calculations, the theoretical side of the team imagined these two independent collections of beats along two separate time lines; each collection is effectively pulsing in its own time dimension. These two time dimensions can be traced on to the surface of a torus. The quasi-periodic nature of the dual time lines becomes clear by the way they each wrap around the torus again and again “at a weird angle that never repeats on itself,” Potter says.
When the team implemented the new program with the quasi-periodic sequence, Quantinuum’s processor was indeed protected for the full length of the test: 5.5 seconds. “It doesn’t sound like a lot in seconds, but it’s a really stark difference,” Bohnet says. “It’s a clear sign the demonstration is working.”
“It’s pretty cool,” agrees Chetan Nayak, an expert on quantum computing at Microsoft Station Q at the University of California, Santa Barbara, who was not involved in the study. He notes that, in general, two-dimensional spatial systems offer better protection against errors than one-dimensional systems do, but they are harder and more expensive to build. The effective second time dimension created by the team sneaks round this limitation. “Their one-dimensional system acts like a higher-dimensional system in some ways but without the overhead of making a two-dimensional system,” he says. “It’s the best of both worlds, so you have your cake and you eat it, too.”
Samuli Autti, a quantum physicist at Lancaster University in England, who was also not involved with the team, describes the tests as “elegant” and “fascinating” and is particularly impressed that they involve “dynamics”—that is, the laser pulses and manipulations that stabilize the system and move its constituent qubits. Most previous efforts to topologically boost quantum computers have relied on less active control methods, making them more static and less flexible. Thus, Autti says, “Dynamics with topological protection is a major technological goal.”
The name the researchers assigned to their new topological phase of matter recognizes its potentially transformative capabilities, although it is a bit of a mouthful: emergent dynamical symmetry-protected topological phase, or EDSPT. “It’d be nice to think of a catchier name,” Potter admits.
There was another unexpected bonus of the project: the original failed test with the periodic pulse sequence revealed that the quantum computer was more error-prone than assumed. “This was a good way of stretching and testing how good Quantinuum’s processor is,” Nayak says.
