Observation of disorder-free localization using a (2+1)D lattice gauge theory on a quantum processor

In the solid world of everyday materials, electricity and heat usually flow freely, like water through a pipe, until something blocks their path. For decades, physicists understood that if a material is perfectly clean and uniform, energy spreads out evenly until the system settles into a calm, predictable state. However, if the material is messy or disordered—filled with random impurities—energy can get stuck, trapped in place as if the pipe were clogged with debris. This phenomenon, known as localization, is a well-known way to stop the flow of energy. For a long time, scientists believed that if particles in a system interacted with one another, this trapping effect would eventually break down, allowing energy to flow again no matter how messy the material was. But recent theories suggested that even in interacting systems, disorder could hold energy captive for incredibly long times, creating a state of matter that refuses to settle down.

A team of researchers at Google Quantum AI and their collaborators has now observed a surprising twist on this idea. They found that energy can become trapped and fail to spread, even when the system is perfectly clean and contains no disorder at all. This discovery, published in a recent study, challenges the intuition that messiness is required to stop the flow of energy. By using a powerful quantum computer, the team simulated a specific type of grid where particles and forces interact in a highly structured way. They watched what happened when they introduced a small burst of energy into the center of this grid. In a normal, clean system, that energy would ripple outward, spreading across the entire grid until it was evenly distributed. Instead, they found that in certain conditions, the energy remained stuck right where it started, refusing to diffuse.

The experiment took place on a superconducting quantum processor, a machine that uses tiny circuits to mimic the behavior of quantum particles. The researchers built a digital model of a lattice, which is essentially a grid of points connected by lines. On this grid, they placed two types of components: "matter" qubits, which act like the particles carrying energy, and "gauge" qubits, which act like the forces connecting them. The team prepared the system in a state that looked perfectly uniform and orderly, with no random variations or impurities. They then created a small disturbance in the middle of the grid, similar to dropping a pebble into a still pond. In a standard, clean system, the ripples from that pebble would travel outward, eventually washing over the entire surface.

What the researchers observed was different. When they prepared the system in a specific way that involved a quantum superposition—a state where the system exists in many possible configurations at once—the energy disturbance did not spread. Instead, it stayed localized near the center of the grid. The energy remained trapped, and the system retained a memory of where the disturbance began, even after many cycles of evolution. This behavior, which the authors call disorder-free localization, occurred in both one-dimensional rings and two-dimensional grids. The key to this phenomenon was not a lack of order, but rather a specific kind of order that mimics the effects of disorder. The system's internal symmetries created an effective background that acted like a random landscape, trapping the energy without any actual randomness being present.

To understand why this happened, the researchers looked at the system through a different lens. They realized that the clean, uniform state they created was actually a superposition of many different possible "disorder" configurations. In most of these hidden configurations, the background potential looked messy and disordered, which is known to trap energy. Because the quantum system was exploring all these possibilities simultaneously, the energy got trapped in the majority of them, leading to an overall effect where the energy could not move. This is distinct from a system where you simply average over many different messy experiments; here, the single, clean experiment naturally produced the trapping effect because of how the quantum states were combined.

The team also measured how the system's internal connections changed over time. They found that the system's "entanglement entropy," a measure of how much the parts of the system are linked together, grew much faster in this disorder-free trapped state than in a typical disordered system. This was a crucial finding because it showed that the trapped state was fundamentally different from the usual "many-body localized" states that scientists have studied for years. In those traditional disordered systems, the connections between parts grow very slowly. In this new disorder-free state, the connections grew rapidly, suggesting a unique type of quantum behavior that is neither fully flowing nor fully stuck in the traditional sense.

The researchers confirmed these findings by running the same experiment on a two-dimensional grid with 81 qubits. Just as in the one-dimensional ring, the energy disturbance remained localized when the system was prepared in the superposition state, while it spread out freely when prepared in a single, non-superposed state. The results were consistent across both dimensions, suggesting that this phenomenon is robust and not just a fluke of a specific setup. The team also compared their experimental data with computer simulations, finding that the real quantum processor behaved in close agreement with the theoretical predictions, even as the system grew larger and more complex.

This work does more than just observe a new state of matter; it offers a new way to study disorder itself. Usually, to understand how a messy system behaves, scientists must run thousands of simulations with different random arrangements of impurities and then average the results. This is computationally expensive and difficult. The researchers showed that by using a quantum superposition, they could effectively sample all possible disorder configurations in a single experiment. This approach could significantly speed up the study of complex materials, allowing scientists to explore rare events and extreme conditions that are currently out of reach for classical computers.

The study highlights a deep connection between the symmetries of a physical system and the way energy moves through it. It demonstrates that you do not need a messy, disordered environment to stop the flow of energy; you only need the right kind of quantum order. This insight could help physicists design new materials or quantum devices that can protect information from spreading and leaking away, a critical requirement for building stable quantum computers. By showing that localization can happen without disorder, the researchers have opened a new chapter in the study of how quantum systems evolve, proving that the absence of chaos can sometimes create the same effects as its presence.