Even though quantum computers are a young technology and aren't yet ready
for routine practical use, researchers have already been investigating the
theoretical constraints that will bound quantum technologies. One of the
things researchers have discovered is that there are limits to how quickly
quantum information can race across any quantum device.

These speed limits are called Lieb-Robinson bounds, and, for several years,
some of the bounds have taunted researchers. For certain tasks, there was a
gap between the best speeds allowed by theory and the speeds possible with
the best algorithms anyone had designed. It's as though no car manufacturer
could figure out how to make a model that reached the local highway limit.

But unlike speed limits on roadways, information speed limits can't be
ignored when you're in a hurry—they are the inevitable results of the
fundamental laws of physics. For any quantum task, there is a limit to how
quickly interactions can make their influence felt (and thus transfer
information) a certain distance away. The underlying rules define the best
performance that is possible. In this way, information speed limits are more
like the max score on an old school arcade game than traffic laws, and
achieving the ultimate score is an alluring prize for scientists.

Now a team of researchers, led by JQI Fellow Alexey Gorshkov, have found a
quantum protocol that reaches the theoretical speed limits for certain
quantum tasks. Their result provides new insight into designing optimal
quantum algorithms and proves that there hasn't been a lower, undiscovered
limit thwarting attempts to make better designs. Gorshkov, who is also a
Fellow of the Joint Center for Quantum Information and Computer Science
(QuICS) and a physicist at the National Institute of Standards and
Technology, and his colleagues presented their new protocol in a recent
article published in the journal Physical Review X.

"This gap between maximum speeds and achievable speeds had been bugging us,
because we didn't know whether it was the bound that was loose, or if we
weren't smart enough to improve the protocol," says Minh Tran, a JQI and
QuICS graduate student who was the lead author on the article. "We actually
weren't expecting this proposal to be this powerful. And we were trying a
lot to improve the bound—turns out that wasn't possible. So, we're excited
about this result."

Unsurprisingly, the theoretical speed limit for sending information in a
quantum device (such as a quantum computer) depends on the device's
underlying structure. The new protocol is designed for quantum devices where
the basic building blocks—qubits—influence each other even when they aren't
right next to each other. In particular, the team designed the protocol for
qubits that have interactions that weaken as the distance between them
grows. The new protocol works for a range of interactions that don't weaken
too rapidly, which covers the interactions in many practical building blocks
of quantum technologies, including nitrogen-vacancy centers, Rydberg atoms,
polar molecules and trapped ions.

Crucially, the protocol can transfer information contained in an unknown
quantum state to a distant qubit, an essential feature for achieving many of
the advantages promised by quantum computers. This limits the way
information can be transferred and rules out some direct approaches, like
just creating a copy of the information at the new location. (That requires
knowing the quantum state you are transferring.)

In the new protocol, data stored on one qubit is shared with its neighbors,
using a phenomenon called quantum entanglement. Then, since all those qubits
help carry the information, they work together to spread it to other sets of
qubits. Because more qubits are involved, they transfer the information even
more quickly.

This process can be repeated to keep generating larger blocks of qubits that
pass the information faster and faster. So instead of the straightforward
method of qubits passing information one by one like a basketball team
passing the ball down the court, the qubits are more like snowflakes that
combine into a larger and more rapidly rolling snowball at each step. And
the bigger the snowball, the more flakes stick with each revolution.

But that's maybe where the similarities to snowballs end. Unlike a real
snowball, the quantum collection can also unroll itself. The information is
left on the distant qubit when the process runs in reverse, returning all
the other qubits to their original states.

When the researchers analyzed the process, they found that the snowballing
qubits speed along the information at the theoretical limits allowed by
physics. Since the protocol reaches the previously proven limit, no future
protocol should be able to surpass it.

"The new aspect is the way we entangle two blocks of qubits," Tran says.
"Previously, there was a protocol that entangled information into one block
and then tried to merge the qubits from the second block into it one by one.
But now because we also entangle the qubits in the second block before
merging it into the first block, the enhancement will be greater."

The protocol is the result of the team exploring the possibility of
simultaneously moving information stored on multiple qubits. They realized
that using blocks of qubits to move information would enhance a protocol's
speed.

"On the practical side, the protocol allows us to not only propagate
information, but also entangle particles faster," Tran says. "And we know
that using entangled particles you can do a lot of interesting things like
measuring and sensing with a higher accuracy. And moving information fast
also means that you can process information faster. There's a lot of other
bottlenecks in building quantum computers, but at least on the fundamental
limits side, we know what's possible and what's not."

In addition to the theoretical insights and possible technological
applications, the team's mathematical results also reveal new information
about how large a quantum computation needs to be in order to simulate
particles with interactions like those of the qubits in the new protocol.
The researchers are hoping to explore the limits of other kinds of
interactions and to explore additional aspects of the protocol such as how
robust it is against noise disrupting the process.

## Reference:

Minh C. Tran et al, Optimal State Transfer and Entanglement Generation in
Power-Law Interacting Systems, Physical Review X (2021).
DOI: 10.1103/PhysRevX.11.031016

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