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.
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Physics