Realization of decoherence-induced averaged symmetry-protected topological phases on quantum processors

In the quantum world, matter can organize itself into shapes that are not defined by the arrangement of atoms, but by the invisible, tangled connections between them. These are called topological phases, and they are remarkably robust; you can stretch, twist, or jiggle the material, and its fundamental nature remains unchanged. For decades, scientists have studied these shapes in perfect, isolated systems where the quantum state is pure and unblemished. In these ideal settings, the stability of the shape relies on a strict rule: a symmetry. Think of this symmetry as a law that the system must obey at every single moment, ensuring that the edges of the material behave in a specific, protected way. However, the real world is rarely perfect. Quantum systems are constantly bombarded by their environment, leading to a loss of information known as decoherence. This noise turns a pure, sharp quantum state into a messy mixture of possibilities. For a long time, physicists believed that this messiness would destroy the delicate topological shapes, washing away the very symmetries that held them together. The prevailing view was that once a system became a mixed, noisy ensemble, its special topological properties would vanish, leaving behind only a trivial, uninteresting state.

A team of researchers has now challenged this assumption by demonstrating that noise, when carefully controlled, can actually create a new kind of topological order. Working with programmable quantum processors, they showed that even when a system is subjected to decoherence, a form of symmetry can survive, not in every single instance, but on average. They started with a one-dimensional chain of quantum bits, arranged in a specific pattern known as a cluster state, which is famous for its protected edges. They then introduced a specific type of noise: a random flipping of the quantum state on every other link in the chain. In any single run of the experiment, this noise scrambled the system, destroying the strict symmetry that usually protects the shape. However, when the researchers looked at the results of thousands of these runs combined, a surprising pattern emerged. The symmetry was not gone; it had simply changed its nature. Instead of being a rigid law that applied to every moment, it became an average law that held true only when the different noisy outcomes were blended together. This new state, which the researchers call an averaged symmetry-protected topological phase, proved that the topological structure was still there, encoded in the statistical mixture of the system, even though it was invisible if you looked at a single noisy snapshot.

To prove this, the team had to invent a new way of looking at the data. Standard measurements, which look at the system once and record the result, failed because the noise caused the signals to cancel each other out. It was like trying to hear a melody by listening to a thousand different people singing it at slightly different times and pitches; the sound would just be a confusing hum. To cut through this confusion, the researchers used a technique that involved preparing two identical copies of the noisy system at the same time. By comparing these two copies in a specific way, they could filter out the random noise and reveal the underlying structure that was hidden in the average. They measured a property called a string correlation, which acts like a long-range thread connecting the ends of the chain. In a single copy, this thread appeared to break and fade as the noise increased. But when they used the two-copy method, the thread remained strong and intact, proving that the topological order had survived the noise. This was a direct observation of a new kind of quantum matter that exists only in the realm of mixed states, where the order is defined by the collective behavior of many possibilities rather than a single, perfect reality.

The researchers also examined the internal energy structure of the system to see how the noise reshaped the quantum landscape. They found that while the noise did change the distribution of energy levels, it did not destroy the characteristic pairing of states that signals the presence of protected edges. In a perfect system, these edge states come in pairs, a signature of the topological protection. When the noise was introduced, the system did not lose this pairing; instead, the noise simply shifted the weight of the system into different sectors, creating a more complex pattern where the paired structure remained visible within each section. This confirmed that the topological protection was robust enough to withstand the engineered decoherence. The experiment was conducted on quantum hardware with chains of up to forty quantum bits, and the results matched the theoretical predictions with high precision. The team demonstrated that by carefully engineering the noise, they could transform a system from having a strict, strong symmetry to having a weaker, average symmetry, without losing the topological order that makes the system special.

This work opens a new door for understanding how quantum matter behaves in the real, noisy world. It suggests that we do not need to eliminate all noise to preserve quantum properties; instead, we might be able to harness noise as a resource. By designing systems where the topological order is protected by average symmetries, we could create more resilient quantum materials that do not require the impossible conditions of perfect isolation. The study provides a clear path for using current quantum processors to explore these mixed-state phases, showing that the messy, decoherent nature of the real world does not necessarily mean the end of quantum order. Instead, it reveals a richer landscape where order can emerge from the average of many chaotic trajectories, offering a new perspective on how to build and protect the quantum technologies of the future.