A hundred years ago, James Clerk Maxwell invented a demon that sorts molecules and violates the second law of thermodynamics. Today its descendants work on quantum lattices: they don't move particles but shuffle errors, turning them into useful work. In a new paper, the surface code becomes a toll bridge along which ergotropy, the maximum work extractable by unitary operations, travels from Alice to Bob without a single quantum of transmitted energy.
Alice holds a charged battery and a rectangular lattice of qubits encoding a logical qubit. She spends energy ΔE to encode it through interaction with a boundary string, then measures the stabilizers and sends Bob a classical record of the syndromes. Upon receiving this record, Bob applies a minimum-weight decoder and, if decoding succeeds, charges his battery. The key point: Bob extracts energy without receiving a single physical qubit, only bits of information.
But the bridge comes at a cost. Causality requires the number of syndrome measurement rounds to grow in proportion to the distance N, so the cost of maintaining the channel W_bulk grows as N² (the numerical exponent is 2.05 ± 0.04). The intersection of the nearly constant ergotropy and the cost parabola yields a thermodynamic horizon N_max ≈ 78 cells, beyond which the net work becomes negative regardless of the code or decoder quality. This is a fundamental limit comparable to Landauer's erasure principle.
Until now it was unclear whether topological order could serve as a channel for nonlocal transfer of useful work at finite temperature, rather than merely protecting qubits. It has now been shown that the surface code allows ergotropy to be teleported between distant nodes using only local operations and classical communication, with the second law of thermodynamics strictly obeyed. The five-stage protocol was verified numerically on the Stim simulator with realistic noise. No practical applications beyond fundamental science are in sight yet, but even today the protocol could be implemented on existing superconducting processors to test fundamental limits of distributed quantum thermodynamics. The quantum demon has learned to teleport work, but it pays for this with quadratically growing infrastructure.
The thermodynamic horizon N_max ≈ 78 cells corresponds to roughly 78×7 = 546 physical qubits in the channel, which already fits on modern superconducting chips. The critical temperature T_c ≈ 0.937 J/k_B, at a typical coupling constant J/h ~ 5–10 GHz, amounts to tens of millikelvins, that is, the operating range of an ordinary dilution refrigerator.
The idea of a nonlocal demon that extracts work from information echoes Stanisław Lem's story 'The Fourteenth Voyage' from The Star Diaries of Ijon Tichy, in which the hero encounters a being that violates the second law of thermodynamics. In this protocol the second law is strictly obeyed, thanks to the quadratic cost of maintaining the channel.