For the archiving of tax and census records, the Incas used a device consisting of a set of cords. With the so-called Quipu, the information could be encrypted in nodes. A few hundred years later, physicists have developed a far more sophisticated modern equivalent of this method, which they have now presented in the journal "Nature". Their "quipu" is a new phase of matter created in a quantum computer. The cords are atoms, and the nodes are formed by patterns of laser pulses that open up a second dimension of time.
At first glance, this seems completely incomprehensible - to make it a little more understandable, you have to go back a little: Usually a phase of matter is a spatial area in which certain material properties are homogeneous - for example the density, arrangement or chemical composition. The newly found phase is now one of many within a family of so -called topological phases that were first identified in the 1980s. The order of these materials is not based on the arrangement of their components - such as the regular distances of the atoms in a crystal - but on their dynamic movements and interactions.
Symmetry in time
New topological phases can be created with the help of new combinations of electromagnetic fields and laser pulses. This brings order or "symmetry" into the movements and states of the atoms of a material. However, such symmetries are primarily in time and not in the room, for example in induced periodic movements. However, temporal symmetries are usually difficult to identify directly. However, they can be discovered mathematically.
To do this, the material must be described as a low-dimensional projection from a hypothetical higher-dimensional space. To understand: Imagine a hologram on a credit card. Actually, it is a two-dimensional object, but it seems to show something three-dimensional at the right angle. The hologram is therefore a low-dimensional projection of a higher-dimensional object.
The newly created phase of matter manifests itself in a strand of ions, which are electrically charged atoms. However, symmetries can only be detected in the arrangement of the ions if they are considered as a material that exists in a higher-dimensional reality with two time dimensions. "It's really exciting to see this unusual phase of matter in a real experiment – especially because the mathematical description is based on a theoretical 'extra' time dimension," says the first author of the publication, Philipp Dumitrescu, who was working at the Flatiron Institute in New York City when the experiments took place.
Second time dimension discovered by chance
Opening up a portal to an additional dimension of time – even if it's just a theoretical one – sounds exciting, but it wasn't the physicists' original plan. "Our motivation was 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 when the team members really had the new phase in mind did they realize its potential: in fact, it could help make data processing in quantum computers less error-prone. How so?
A short digression to understand the answer: Process and store classic standard computers in the form of episodes from zeros and one, the bits. The enormous performance of quantum computers, on the other hand, is based on quantum bits that can take on values of 0 or 1 or any overlay states. (Think of Schrödinger's cat, which can be both dead and alive.)
Most quantum computers encode information in the state of each individual quBIT, for example in an internal quantum property of a particle. This can be, for example, the spin, which either shows up or down what a 0 or 1 corresponds. In addition, it can also be in an overlay state of these two orientations. The high susceptibility to interference of such systems is problematic: every noise, for example an undesirable magnetic field, would destroy a carefully prepared quantum system by randomly turning the spins back and forth. The quantum effects would be ruined and the calculations would be broken.
Potter compares this susceptibility to interference with the transmission of a message with the help of fine strings, with each string having the shape of a single letter and laid out on the ground. The readability is good until a small breeze comes, he says. Because now some letters are completely gone or at least no longer recognizable.
Quantum mechanical information interwoven in the material
In order to develop a more error -resistant quantum material, Potter's team turned to the topological phases. In a quantum computer that exploits the topology, the information is not coded locally in the state of each individual quBIT, but woven into the material globally. "It is similar to a knot that is difficult to solve - like Quipu, the mechanism of the Incas for saving numbers and other data," says Potter.
Topological phases are fascinating because they can protect against errors that are actually a property of the material, adds study co-author Justin Bohnet, a quantum physicist at Quantinuum in Broomfield, Colorado, where the experiments took place. This is different from traditional error correction protocols, where you constantly take measurements on small parts of the system to see if errors occur and then go and correct them."
Quantinuum's H1 quantum processor consists of a strand of ten ytterbium ions in a vacuum chamber. Laser control the positions and states of these ten qubits exactly. Experts speak of an "ionenfalle" - a standard technique that physicists use to manipulate ions. In their first attempt to create an error -stable topological phase, Potter, Dumitrescu and her colleagues try to give the processor a simple time -symmetry. For the purpose, they missed the ions, all of which are lined up in a dimension, with regular recurring laser impulses periodic bumps. "Our calculations showed that this would protect [the quantum processor] from mistakes," says Potter. It is similar to that when an even drum strike keeps several dancers in rhythm.
At first, nothing worked out: the malfunctions got worse
To control whether they were right, the researchers let the program run on the Quantinuum processor several times and checked every time the resulting quantum state of all quBITs matched their theoretical predictions. "It didn't work at all," says Potter and laughs. "Completely incomprehensible stuff came out." Whenever mistakes accumulated in the system, his performance deteriorated within 1.5 seconds. The team soon recognized: it was not enough to add only one time symmetry. Instead of preventing the quables from being impaired by bumps and noise from the outside, the periodic laser pulses increased the tiny swallowing in the system and made small disturbances worse, explains Potter.
So he and his colleagues turned back to the drawing board until they finally had an insight: if there was a pattern of pulses that is not random, but somehow ordered, but does not repeat regularly, they could create a more resilient topological phase. They calculated that such a "quasi-periodic" pattern could potentially produce multiple symmetries in the processor's ytterbium qubits while avoiding the unwanted amplifications. As a pattern, they chose the mathematically well-studied Fibonacci sequence, in which the next number in the sequence is always the sum of the two previous ones. So while a regular periodic laser pulse sequence could switch between two frequencies of two lasers as "A, B, A, B, ...", a pulsating Fibonacci sequence would run as "A, AB, ABA, ABAAB, ABAABABA, ...".
This pattern actually arises from a fairly complex arrangement of two collective different laser pulses. Nevertheless, according to Potter, the system can simply be viewed as "two lasers", "pulsating with two different frequencies" and ensuring that the pulses never overlap in time. For the calculations, the team introduced itself in theory that these two independent pulse collectives run along two separate templates; Each collective effectively pulsates in its own time dimension. The two time dimensions can be traced on the surface of a gate, i.e. a donut -shaped structure. Based on the way they always wrap around the Torus, the quasiporiodic nature of the two templates becomes clear, "in a strange angle that never repeats itself," says Potter.
When the team implemented the new program with the quasi-periodic sequence, the Quantinuum processor was actually protected for the entire duration of the test: 5.5 seconds long. "It doesn't sound like much, but it makes a clear difference," says Bohnet. "This is a clear proof that the demonstration works.«
The best of two worlds combine
Chetan Nayak, an expert in quantum computing at "Microsoft Station Q" at the University of California, Santa Barbara, who was not involved in the study, also agrees: "That's pretty cool." He notes that two-dimensional spatial systems generally provide better protection against errors than one-dimensional systems, but they are more difficult and more expensive to build. The effective second time dimension created by the team bypasses this limitation. "Your one-dimensional system behaves like a higher-dimensional system in some respects, but without the hassle associated with making a two-dimensional system," says Nayak. "It's the best of both worlds, so you can not only enjoy the cake, but also eat it," he jokes.
Samuli Authi, a quantum physicist at the University of Lancaster in England and also not part of the team, describes the tests as "elegant" and "fascinating". Authi is particularly impressed by the fact that the attempts contain a "dynamic" - that is, the laser pulses and manipulations that can stabilize the system and move its individual qubits. Most of the previous attempts to strengthen quantum computers topologically have based less active control methods, which makes them static and less flexible. "Dynamics in combination with topological protection against disorders is therefore an important technological goal," says Autti.
The name given by the researchers to their new topological phase of matter is somewhat awkward: "Emergent Dynamical Symmetry-Protected Topological Phase" or "EDSPT". It would be nice if we could come up with a more memorable name, Potter admits. An unexpected bonus of the project: the originally failed test with the periodic pulse sequence showed that the quantum computer was more error-prone than assumed. "This is a good way to test how well the Quantinuum processor is working," says Nayak.
© Springer Nature Limited Scientific American, New Phase of Matter Open's Portal to Extra Time Dimension, 2022
