In 1867, James Clerk Maxwell imagined a demon that sorts gas molecules and thereby violates the second law of thermodynamics. The demon needs to know the speeds of the particles. In the quantum world, a similar task arises: keep entanglement from growing like an avalanche, but you cannot observe the entire system. It turns out the demon only needs an incomplete notebook.
Quantum entanglement is a quantum connection in which particles lose their independence. In a stabilizer circuit of N qubits, at each step the agent applies an optimally disentangling two-qubit gate with probability p, and a random Clifford gate with probability 1-p. The agent sees a "scoreboard" of stabilizers from which a fraction 1-q of rows has been randomly removed. Training with Proximal Policy Optimization and a transformer architecture gave an unexpected result: with full information (q=1), the phase transition disappears completely. For any arbitrarily small p>0, the steady state exhibits an area-law entanglement, and the volume-law phase shrinks to the point p=0.
The mechanism is the creation of a sequence of "bottlenecks": the agent selects a few equally spaced bonds and keeps entanglement nearly zero on them. This splits the chain into subsystems and limits the maximum achievable entanglement. The entanglement profile takes the form of pyramids that are self-similar when the system size is doubled. With partial information, a critical threshold $q_c$(p) is found: above it, area law; below it, volume law. As p increases, the required fraction of information decreases. For p≥$p_c^{gree}$dy, the area law persists even as q→0, because the agent effectively catches Bell pairs using the only available stabilizer.
Before this work, it was unclear whether entanglement in a many-body quantum system could be controlled with only partial information about its state, and what strategies would be needed. Now it is shown that trained reinforcement-learning agents can maintain area-law entanglement even with a small fraction of observed stabilizers, provided that fraction is above the critical threshold. Comparing random, greedy, and trained strategies on the same model with varying fractions of available information revealed a sharp transition in the system's behavior. This could be useful in developing protocols for quantum error correction and quantum memory, where one needs to suppress entanglement with noise while having limited access to measurements.
Maxwell's demon with an incomplete notebook turned out to be not a fantasy but a concrete algorithm. Next steps include determining critical exponents near the information threshold and testing strategies on circuits with continuous gate parameters, moving closer to real quantum processors.
For a system of 128 qubits, the trained agent uses only about 13 stabilizers out of 128 (at q=0.1) and still maintains area-law entanglement, catching Bell pairs with a probability of 76%.
The idea of a "demon" that, knowing only part of the information about a system, keeps it from chaos, resembles Maxwell's demon from science fiction, but here the demon is a neural network trained by trial and error.