Researchers at Zhejiang University and the University of Leeds found recurring patterns within chaotic quantum systems. Published in Nature Physics, the study used a quantum processor to identify stable motion. Zlatko Papić said, "Understanding when and how they resist this fate is one of the difficult questions we have been exploring."
Many complex quantum systems rapidly lose the recognizable patterns of their initial states as their components interact. To describe patterns of regular and chaotic motion in specific systems, physicists can construct a mathematical map called an effective phase space.
In some classical systems that follow familiar laws of motion, orderly and chaotic paths occupy different regions of phase space. Yet establishing whether a comparable pattern exists in quantum many-body systems (i.e., systems with many interacting quantum components) has so far proved challenging, partly because interactions in these systems can produce a quantum phenomenon called entanglement.
When parts of a system are entangled, their combined quantum state cannot be fully described by treating each independently.
Researchers at Zhejiang University and the University of Leeds have devised a new approach to search for recurring patterns of activity in complex, chaotic quantum many-body systems. This approach, outlined in a paper published in Nature Physics, was successfully used to identify a stable recurring pattern in a quantum processor with multiple interacting qubits.
"This work grew out of our long-standing collaboration with Zhejiang University on using quantum processors to understand what happens when many quantum particles interact and evolve together," Zlatko Papić, senior author of the paper, told Phys.org.
"Normally, such systems rapidly lose memory of how they started. Understanding when and how they resist this fate is one of the difficult questions we have been exploring."
Searching for regular motion in quantum chaos
This recent study builds on earlier research by Papić and his collaborators at Zhejiang University and the University of Leeds. In their earlier work, the team showed that some starting states in a 30-qubit superconducting processor could repeatedly return to a recognizable pattern, instead of settling into the disordered behavior typically associated with complex interacting quantum systems—a behavior known as "quantum scars."
"In our first joint paper on quantum scars, published in Nature Physics, we demonstrated this unusual phenomenon on a superconducting quantum processor: a specially prepared system repeatedly returned close to its starting configuration," said Papić.
"That work led us to ask whether these unusual motions could be part of a much richer landscape, and whether a quantum processor could take an active role in discovering it."
Drawing inspiration from their previous observations, the researchers set out to develop a method to search for hidden patterns of regular motion within otherwise chaotic quantum behavior, or, in other words, identify "islands" of regular motion in a "sea" of quantum chaotic behavior.
The researchers tested their approach on a 24-qubit ladder system selected from a superconducting quantum processor containing more than 100 qubits. The processor worked together with an ordinary computer in a repeated loop.
"We prepared the quantum system, let it evolve briefly, and collected measurements," explained Papić. "The ordinary computer then uses those measurements to find a relatively simple quantum state that closely matches the result. We prepare this updated state on the processor and repeat. Over successive rounds, this process can home in on motion that repeats regularly, without our having to specify that motion in advance."
The researchers' approach was inspired by an algorithm called ScarFinder, introduced in a previous paper published in PRX Quantum. This algorithm searches for unusual, recurring patterns of motion associated with quantum many-body scars in interacting quantum systems.
"Our postdocs Jie Ren and Andrew Hallam played a central role: their expertise in tensor networks, mathematical tools for describing complicated quantum states compactly, was crucial to developing the approach," explained Papić.
"Our Zhejiang collaborators, in particular Hang Dong, then implemented the protocol using 24 superconducting quantum bits, or qubits. Starting from an irregular pattern of motion, the feedback successfully guided the system toward a repeating one."
A key advantage of the team's approach is that every round it performs requires only a short period of quantum evolution and simple measurements of individual qubits. Moreover, it can be applied to current processors, which struggle to preserve delicate quantum behavior for long periods.
A new approach for studying complex quantum systems
This study introduces and experimentally demonstrates a method for investigating how order and chaos coexist in complex many-body quantum systems. Using this method, the team was able to uncover and stabilize recurrent activity in a 24-qubit system.
"The most striking finding is that there exist whole 'islands' of regular motion within a sea of chaotic behavior," said Papić. "This structure of regular motion coexisting with chaos is very common in classical systems, e.g., the solar system works like this (planets move seemingly periodically, while the system's overall motion is chaotic and impossible to predict at very late times). However, analogous structures in quantum many-body systems have not been observed prior to our work."
The researchers found that the regular paths they observed changed shape as they adjusted the interactions between qubits. Their feedback loop approach unveiled and stabilized recurring patterns that were already present in a system's underlying dynamics.
"Our approach gives us a practical way to explore this landscape experimentally," said Papić. "A broader implication of this study is that quantum processors can serve as instruments of scientific discovery. Learning how to find and control these regular motions could eventually help us preserve useful quantum behavior for longer."
Papić and his colleagues are now planning more research aimed at understanding how widespread the behavior they observed is. Specifically, they would like to determine which kinds of quantum systems support the observed regular islands, what determines their stability and how the islands change as the number and arrangement of qubits vary.
"We also want to clarify the relation of this phenomenon with quantum scars," added Papić. "Are some previously observed scars special cases within a broader landscape of regular motion, and when are the two phenomena distinct? Combining theoretical tools such as ScarFinder with experiments on quantum processors gives us a promising way to investigate these questions."