Quantum Chaos Kicks in Sooner Than Previously Thought

The process of scrambling two eggs—cracking them, whisking the yolk and whites, pouring the liquid into a frying pan, and stirring—can take several minutes. One can watch the process unfold and learn a bit about how the scrambling occurs. Now, a new theoretical paper in Science shows that, under the right conditions, the subatomic equivalent of eggs could become scrambled in the blink of an eye.

"Quantum dynamics have the ability to scramble exponentially faster than any dynamics in the classical world," says lead author Thomas Schuster, a Sherman Fairchild Postdoctoral Scholar Research Associate in Theoretical Physics at Caltech. Schuster worked on the project with Hsin-Yuan (Robert) Huang (PhD '24), an assistant professor of theoretical physics at Caltech and a William H. Hurt scholar.

"This is a big surprise and goes against our intuition," Schuster says. "We thought it would take more time."

In any quantum material, the various subatomic particles making it up interact and undergo distinctly quantum phenomenon, such as entanglement and superposition. As a quantum system evolves over time, the state of the system and the information contained within it becomes increasingly jumbled as different parts of the system get entangled with one another.

Generating quantum randomness is a useful tool in quantum cryptography, and in studying quantum systems in general. Schuster wanted to study the question of how hard or easy it would be to learn about quantum states once the information had started to scramble.

As Schuster, Huang, and their colleague Jonas Haferkamp of Harvard University and Saarland University in Germany developed a mathematical proof for how hard it is to learn about a quantum system as it scrambles, they realized they had discovered something else: that quantum systems very quickly become completely unrecognizable—what scientists call "maximally random."

"This ultrafast scrambling occurs when quantum systems can explore the space of all possibilities," Huang explains. "Nothing in the classical world mimics this scrambling behavior, and even some restricted quantum worlds, such as those restricted to real numbers, cannot mimic this. The ultrafast scrambling means it is much harder to learn about the system's evolution time, entanglement, and other features than we thought before."

On the positive side, the result may help in future quantum applications, including those in cryptography as well as in the quest to establish quantum advantage—experimental demonstrations in which quantum computers outperform their classical counterparts.

For example, Google demonstrated quantum advantage in 2019 using the same type of quantum randomness generated in this study.

"This result reveals that quantum devices can demonstrate quantum advantage using significantly smaller quantum circuits than previously anticipated," Huang says. "This may enable a broader range of quantum devices to achieve quantum advantages."

The study titled "Random unitaries in extremely low depth" was funded by the Walter Burke Institute for Theoretical Physics at Caltech, Harvard, MIT, the US Department of Energy Quantum Systems Accelerator, and Caltech's Institute for Quantum Information and Matter (IQIM), a US National Science Foundation Physics Frontier Center.