Quantum Computer Weaves an Invisible Thread of Order express
A rope braided from a hundred short strands can be twisted to the right or to the left. Each strand individually doesn't know which way the whole rope is twisted, but try to unravel it, and the difference immediately shows. That's roughly how the states physicists call symmetry-protected are arranged: locally they are indistinguishable, but globally they are different.
A group of researchers took a chain of a hundred spins — tiny magnetic arrows that can point up or down. The spins alternated: strong coupling, weak coupling, strong again. Such a chain can exist in two different hidden phases, and both were prepared on an IBM quantum processor with an accuracy of 97.9–99.0%.
Three independent signatures helped verify that the phase was indeed the right one. The first is nonlocal string order: if you measure every other spin over a length of up to twenty sites, a strict pattern emerges, even though neighboring spins don't show it. The second is the entanglement spectrum: it has characteristic repeated levels, like a symmetric ornament. The third is edge modes: at the ends of the chain, "free" spins appear that are protected by symmetry from disturbances.
Previously, such states were only obtained in computer simulations or in very small systems. Now they can be prepared on real quantum hardware and, possibly, we can study what happens when the system changes abruptly in time, a task that is impossible for ordinary computers.
Original abstract
as written by the authors arXiv:2603.06325
Symmetry-protected topological (SPT) phases extend the Landau paradigm of quantum matter by admitting distinct symmetry-preserving phases that lack any local order parameter. Demonstrating these phases at scale on programmable quantum processors is a key milestone in using quantum hardware to probe emergent many-body phenomena, yet it is impeded by the circuit depth normally required to capture non-trivial entanglement. Here we use a tensor network based approximate quantum compiling (AQC) protocol to construct shallow quantum circuits (18-39 CNOT depth), which prepare 100-site ground states of the spin-1/2 bond-alternating Heisenberg chain in both SPT phases, to 97.9-99.0% fidelity. Upon executing the circuits on IBM quantum hardware, the resulting states exhibit all defining signatures of SPT order including non-local string order for strings of up to length 20, characteristic degeneracies in the entanglement spectrum and clear evidence of symmetry-protected edge modes. The simultaneous observation of these independent diagnostics establishes current quantum computers as versatile platforms for large-scale studies of symmetry-protected quantum matter. More broadly, our results establish a practical foundation for probing non-equilibrium quench dynamics of such systems in regimes that challenge classical computational methods.
A chain of a hundred spins has $2^{100}$ possible configurations — more than the number of atoms in the visible Universe, yet the desired state was set with just a few dozen operations.