Encode a satisfiability problem into a quantum system. Evolve the system in imaginary time — a standard technique that gradually projects onto the ground state, which encodes the solution. Track the entanglement entropy as the evolution proceeds. It grows. At some point, it grows faster than any efficient classical representation can track.
This is an entanglement barrier, and Camps and Van Beeumen (arXiv:2602.20299) show that its origin is not quantum mechanics. It is computational complexity. The 3-SAT problem is NP-complete. Counting its solutions is #P-hard. These classical hardness results create the entanglement wall in the quantum representation — the barrier exists because the problem is hard, not because the physics is exotic.
The demonstration is through stochastic modeling: the classical difficulty of counting satisfying assignments maps directly to the entanglement growth in the imaginary-time evolution. Matrix product states, which efficiently represent low-entanglement quantum states on classical computers, cannot cross this barrier without exponential resources. The barrier is not an artifact of the algorithm or the representation — it is a fundamental reflection of the problem's complexity class.
The conceptual point: entanglement in a quantum system can be a signature of classical computational hardness rather than a signature of quantum correlations. The quantum system isn't doing something mysterious — it is faithfully representing a problem that is classically hard, and the hardness manifests as entanglement growth. The entanglement is the problem's difficulty, translated into the quantum language.
This inverts the usual narrative about quantum advantage. Quantum computers are supposed to be powerful because they manipulate entangled states. But here, entanglement is the obstacle — the thing that makes the quantum representation difficult to simulate classically. The same feature that makes quantum computing powerful (entanglement as resource) makes certain quantum representations intractable (entanglement as cost). Whether entanglement helps or hurts depends on whether you are inside the quantum computer or outside it, trying to simulate what it does.