Understanding Quantum Speed Limits

Unlike signs on the highway, most speed limits in physics cannot be disobeyed. No matter how little you care about getting a ticket, you can never go faster than, for example, the speed of light. Similarly stringent limits exist for information, but depending on how it’s stored and transmitted, there can be slower limits in practice, like the speed of sound—or of a carrier pigeon.

The story gets particularly subtle when the information is quantum. Quantum information is represented by qubits (the quantum version of bits, the ordinary units of information stored in a computer), and can be stored in photons, atoms or other systems governed by the rules of quantum physics. Figuring out how fast information can move from one qubit to another not only makes for interesting science, but is also important for more practical purposes, like improving quantum computers and learning what their limitations might be.

Now, a group of University of Maryland researchers led by Alexey Gorshkov—a fellow of the Joint Quantum Institute (JQI) and the Joint Center for Quantum Information and Computer Science, and a physicist at the National Institute of Standards and Technology—in collaboration with teams at the University of Colorado Boulder, Caltech and the Colorado School of Mines, has found something surprising: The speed limit for quantum information can depend on the task at hand. They detail their results in a paper published this week in the journal Physical Review X and featured in Physics.

Just as knowing the speed of light doesn’t automatically let us build rockets that can travel that fast, knowledge of the speed at which quantum information can travel doesn’t tell us how it can be done. But it allowed the team to devise new information transfer methods that approach the theoretical speed limit closer than ever before.

“Figuring out the fastest way to move quantum information around will help us maximize the performance of future quantum computers,” said Minh Tran, a graduate student in physics at UMD and the lead author of the paper.

One procedure that is subject to these new limits is like a quantum version of cut-and-paste: moving the information stored in one qubit to a different one far away. It’s a crucial task that can become a bottleneck as quantum computers get larger and larger.

In quantum computers based on superconductors, like Google's Sycamore, qubits only talk to other qubits next door—short-range interactions, in physics-speak. That means that once you cut a qubit, you’d have to go door to door, cutting and pasting to adjacent qubits until you reach the target. The speed limit for this situation, found back in the 1970s, is strict and consistent—it doesn’t ease up, no matter how far the information travels.

Things get more complicated—and more realistic for a lot of quantum computing platforms—when considering long-range interactions: qubits that talk not only to those directly next to them, but also to neighbors several doors down. Quantum computers built with trapped ions (such as those built by JQI fellow and Distinguished University Professor Chris Monroe), as well as polar molecules, and Rydberg atoms all have these long-range interactions.

Previous work has shown that in long-range interacting setups, there isn’t always a strict speed limit, other than the speed of light. It depends on the dimensions of the quantum computer, as well as the strength of the long-range interaction.

Finding regimes where these long-range interactions relax the information speed limits carries the promise of making quantum processing much faster. Gorshkov, Tran and their collaborators looked more closely at the regime where information is allowed to travel faster as it gets farther from its origin. For some applications, the speed limit was indeed loose as previously discovered. But for others, it was just as strict as in the case of the nearest neighbor.

This implies that for the same quantum computer, the speed limits are different for different tasks. And even for the same task, such as quantum cut-and-paste, different rules can apply in different situations. If you cut-and-paste in the beginning of a computation, the speed limit is loose, and you can do it very quickly. But if you have to do it mid-computation, when the states of the qubits along the way aren’t known, a stricter speed limit applies.

“The existence of different speed limits is cool fundamentally because it shows a separation between tasks that seemed very similar,” says Abhinav Deshpande, a graduate student in physics at UMD and one of the authors of the new paper.

So far, few experimental realizations of quantum computers have been able to take advantage of long-range interactions. Nevertheless, the state of the art is improving rapidly, and these theoretical findings may soon play a crucial role in designing quantum computing architectures and choosing protocols that optimize their efficiency.

“Once you get systems that are larger and more coherent,” says Gorshkov, “down the road, these insights will be even more applicable.”

Additional reporting contributed by Chad Boutin (NIST).