However, not all questions about quantum systems are easier to answer using quantum algorithms. Some are equally easy for classical algorithms running on regular computers, while others are difficult for both classical and quantum algorithms.
To understand how quantum algorithms and the computers that can run them can benefit, researchers can analyze mathematical models called spin systems, which capture the fundamental behavior of arrays of interacting atoms. It often happens. You might then ask, what happens if you leave the spin system at a certain temperature? The state it settles into, called thermal equilibrium, determines many of its other properties, so researchers have long sought to develop algorithms to find it.
Whether these algorithms actually benefit from being quantum depends on the temperature of the spin system in question. At very high temperatures, the work can be easily done with known classical algorithms. As temperatures drop and quantum phenomena become stronger, the problem becomes more difficult. Some systems become too difficult for even a quantum computer to solve in a reasonable time. However, all these details remain unclear.
“When do we go to a space where we need a quantum, and when do we go to a space where a quantum is useless?” said Ewin Tan, a researcher at the University of California, Berkeley, and one of the authors of the new results. “It’s not very well known.”
In February, Tan and Moitra started thinking about the thermal equilibrium problem with two other MIT computer scientists, a postdoctoral researcher named Ainesh Bakshi and Moitra’s graduate student Allen Liu. In 2023, they were all collaborating on breakthrough quantum algorithms for other tasks involving spin systems and were looking for new challenges.
“When we work together, things just flow,” Bakshi said. “It was great.”
Before their breakthrough in 2023, the three MIT researchers had never worked on a quantum algorithm. 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 their relative naivety as an asset, a way to see problems with fresh eyes. “One of our strengths is that we don’t know much about quantum,” Moitra says. “The only quantum that we know is the one that Eowyn taught us.”
The team decided to focus on relatively high temperatures, where researchers suspected a fast quantum algorithm existed, even though no one could prove it. Soon, they discovered how to adapt old techniques from learning theory to new, faster algorithms. However, while writing the paper, another team also published similar results. This was proof that a promising algorithm developed the previous year worked well at high temperatures. They had been scooped up.
sudden death reborn
Although a little disappointed in coming second, Tan and his collaborators continued to correspond with Álvaro Alhambra, a physicist at the Institute of Theoretical Physics in Madrid and one of the authors of the rival paper. I started. They wanted to understand the differences in the results they achieved on their own. But when Dr. Alhambra read preliminary drafts of the four researchers’ proofs, he was surprised to discover that they had proved something else at an intermediate stage. That is, in a spin system in thermal equilibrium, entanglement disappears completely when a certain temperature is exceeded. “I told them, ‘Oh, this is very, very important,'” Alhambra said.
From left: Allen Liu, Ainesh Bakshi, and Ankur Moitra collaborated with Tang, drawing on their backgrounds in different areas of computer science. “One of our strengths is that we don’t know much about quantum,” Moitra says.
Photo: From left: Courtesy of Allen Liu. Amartya Shanka Biswas. Gretchen Ertl
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