Computer Scientists Prove That Heat Destroys Quantum Entanglement
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Welcome to the Quantascience Podcast. Each episode we bring you stories about developments in science and mathematics. I'm Susan Vallett. While devising a new quantum algorithm, four researchers accidentally established a hard limit on the spooky phenomenon. That's next.

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Nearly a century ago, physicist Erwin Schrödinger called attention to a quirk of the quantum world that has fascinated and vexed researchers ever since. When quantum particles such as atoms interact, they shed their individual identities in favor of a collective state that's greater and weirder than the sum of its parts. This phenomenon is called entanglement.

Yuen Tang is a researcher at the University of California, Berkeley. People don't know what entanglement is, right? Like that's like one of the central mysteries of quantum information. People have been trying to understand this thing for a long time. Researchers have a firm understanding of how entanglement works in idealized systems containing just a few particles. But the real world is more complicated.

In large arrays of atoms, like the ones that make up the stuff we see and touch, the laws of quantum physics compete with the laws of thermodynamics. Things get messy. At very low temperatures, entanglement can spread over long distances, engulfing many atoms and giving rise to strange phenomena such as superconductivity.

Crank up the heat, though, and atoms jitter about, disrupting the fragile links that bind entangled particles.

physicists have long struggled to pin down the details of this process. Now, a team of four researchers has proven that entanglement doesn't just weaken as temperature increases. Rather, in mathematical models of quantum systems, such as the arrays of atoms and physical materials, there's always a specific temperature above which it vanishes completely.

Ankur Moitra of MIT is one of the authors of the new result. What we show is that all of the entanglement is gone. It's zero. It's not just that it's exponentially small. There's nothing there. Researchers had previously observed hints of this behavior and dubbed it the sudden death of entanglement. But their evidence was mostly indirect. The new finding establishes a much stronger limit on entanglement in a mathematically rigorous way.

Curiously, the four researchers behind the new result aren't even physicists. They didn't set out to prove anything about entanglement. They're computer scientists who stumbled on the proof accidentally while developing a new algorithm. Regardless of their intent, the results have excited researchers in the area. Suwon Choi is a physicist at MIT. What they are saying is no matter how you divide the system into different parts, everything is completely classical.

So it's a very strong statement, and I was very impressed by that. The team made their discovery while exploring the theoretical capabilities of future quantum computers. These are machines that will exploit quantum behavior, including entanglement and superposition, to perform certain calculations far faster than the conventional computers we know today. One of the most promising applications of quantum computing is in the study of quantum physics itself.

Let's say you want to understand the behavior of a quantum system. Researchers need to first develop specific procedures, or algorithms, that quantum computers can use to answer your questions. But not all questions about quantum systems are easier to answer using quantum algorithms. Some are equally easy for classical algorithms, which run on ordinary computers, while others are hard for both classical and quantum ones.

To understand where quantum algorithms and the computers that can run them might offer an advantage, researchers often analyze mathematical models called spin systems. These capture the basic behavior of arrays of interacting atoms. They then might ask, "What will a spin system do when you leave it alone at a given temperature?"

The state it settles into is called its thermal equilibrium state. This state determines many of the system's other properties, so researchers have long sought to develop algorithms for finding equilibrium states. Whether those algorithms really benefit from being quantum in nature depends on the temperature of the spin system in question. At very high temperatures, known classical algorithms can do the job easily.

The problem gets harder as temperature decreases and quantum phenomena grow stronger. In some systems, it gets too hard for even quantum computers to solve in any reasonable amount of time. But the details of all this remain murky. Iwen Tang, one of the authors of the new result, says the question is, when do you go to the space where you need quantum, and when do you go to the space where quantum doesn't even help you? Tang says not that much is known.

Last February, Tang and Moitra began thinking about the thermal equilibrium problem together with two other MIT computer scientists, a postdoctoral researcher named Inej Bakshi and Moitra's graduate student, Alan Liu.

In 2023, they'd all collaborated on a groundbreaking quantum algorithm for a different task involving spin systems, and they were looking for a new challenge. Here's Bakshi. This is an excellent set of collaborators to work with, and everyone brings in this incredible insight based on what their background is. When we work together, things just kind of flow. Before that 2023 breakthrough, the three MIT researchers had never worked on quantum algorithms.

Their background was in learning theory, a subfield of computer science that focuses on algorithms for statistical analysis.

But like ambitious upstarts everywhere, they saw the problem with fresh eyes. Here's Moitra. At the end of the day, one of our strengths is that we don't know much quantum, or at least the only quantum we know is the quantum that Ewan taught us. But I think that gives us an advantage because it means that we have this rich body of analogies with classical tools.

That gives us a lot of cause for optimism. The team decided to focus on relatively high temperatures, where researchers suspected that fast quantum algorithms would exist even though nobody had been able to prove it. Soon enough, they found a way to adapt an old technique from learning theory into a new fast algorithm.

But as they were writing up their paper, another team came out with a similar result: a proof that a promising algorithm developed the previous year would work well at high temperatures. They'd been scooped. They were a bit bummed that they'd come in second. So Tang and her collaborators began corresponding with Alvaro Alhambra, a physicist at the Institute for Theoretical Physics in Madrid and one of the authors of the rival paper.

They wanted to work out the differences between the results they'd achieved independently. But when Alhambra read through the preliminary draft of the four researchers' proof, he was surprised to discover that they'd proved something else in an intermediate step. In any spin system in thermal equilibrium, entanglement vanishes completely above a certain temperature. Alhambra says he told the group that what they'd found is very, very important.

the team quickly revised their draft to highlight the accidental result. Here's Moitra. It turns out that this just falls out of our algorithm that we get more than what we bargained for. Researchers had observed this sudden death of entanglement since the 2000s in experiments and simulations on ordinary classical computers.

But none of those earlier works could measure the disappearance of entanglement directly. They had also studied the phenomenon only in small systems, which aren't the most interesting ones. Alhambra says it could have been that for larger and larger systems, you would have to go to higher and higher temperatures to see entanglement disappear. In that case, the sudden death phenomenon might happen at such high temperatures as to be irrelevant in real materials.

The only previous theoretical limit, from 2003, left open that possibility. Instead, Tang and her collaborators showed that the temperature at which entanglement vanishes doesn't depend on the total number of atoms in the system. The only thing that matters is the details of the interactions between nearby atoms. The approach they used in their proof was itself unusual.

Most algorithms for finding thermal equilibrium states are inspired by the way real physical systems approach equilibrium.

but Teng and company used techniques far removed from quantum theory. Nikhil Srivastava is a computer scientist at UC Berkeley. Nikhil Srivastava: This paper, to me, I think what's amazing about it is, yeah, the proof is based on some very algorithmic ideas. And in a way, the proof kind of just ignores the physics. It's just a matrix. Do induction. Do probability and do new algebra. I feel like if you had a lot of physical intuition around these things,

You might try to have a proof in which every step makes physical sense. And this proof of theirs doesn't necessarily make physical sense. In the end, it's very empowering to kind of forget that it's a state. The four researchers' proof that high-temperature spin systems lack any entanglement helps explain another interesting feature of their new algorithm: very little of it is actually quantum.

True, the algorithm's output, a full description of how the atoms in a spin system are oriented in thermal equilibrium, is too unwieldy to store on a classical machine. But other than the last step that generates this output, every part of the algorithm is classical. Here's grad student Alan Liu, who was on the research team. The point is you run...

purely classical processing. And then at the end, you just output an unentangled quantum state. So technically, okay, your output is a quantum state. So you have to have some quantum computation to be able to output this state. But it is like essentially the most trivial quantum computation. And almost everything is happening classically. Tang has a long track record of discovering de-quantization results, meaning proofs that quantum algorithms aren't actually necessary for many problems.

She and her collaborators weren't trying to do that this time, but the proof of vanishing entanglement that they stumbled into amounts to an even more extreme version of de-quantization. It's not just that quantum algorithms don't offer any advantage in a specific problem involving high temperature spin systems. It's that there's nothing quantum about those systems whatsoever. But that doesn't mean quantum computing researchers should lose hope.

Two recent papers identified examples of low-temperature spin systems, in which quantum algorithms for measuring equilibrium states outperform classical ones, though it remains to be seen how widespread this behavior is. And even though Bakshi and his collaborators proved a negative result, the unorthodox method they used to get there indicates that fruitful new ideas can come from unexpected places.

Ankur Moitra says he's an algorithm person, so he loves the discovery of new algorithms that provably solve problems. And you know, that's what's exciting to me about the space and quantum information theory is that there are algorithmic problems, which we can be optimistic that there are crazy new algorithms to be discovered, and that in the process we can discover some beautiful mathematics along the way.

Arlene Santana helped with this episode. I'm Susan Vallett. For more on this story, read Ben Brubaker's full article, Computer Scientists Prove That Heat Destroys Quantum Entanglement, on our website, quantummagazine.org. Make sure to tell your friends about the Quanta Science Podcast and give us a positive review or follow where you listen. It helps people find this podcast.