Maxwell’s Demon Goes Quantum

Maxwell’s demon, the microscopic imp dreamed up by James Clerk Maxwell in 1871 in a rumination about the meaning of the classical second law of thermodynamics, has spurred argument among physicists ever since. Now, researchers in Russia, Switzerland and the United States have formulated a design for a quantum version of the demon—one, they believe, that could have some interesting applications in quantum computing and temperature control at the nanoscale (Phys. Rev. B, doi: 10.1103/PhysRevB.98.214502).

As envisioned, the team’s “extended quantum Maxwell’s demon” would, across a distance as great as five meters, allow a qubit in a mixed quantum state to be replaced with a lower-entropy, pure-state qubit, with no change in energy. But don’t worry: the second law of thermodynamics is still doing just fine.

Microscopic mischief

The demon in Maxwell’s famous thought experiment is an imaginary, very small being who operates a tiny trap door between two closed gas reservoirs, within a box at thermal equilibrium. When the demon sees a gas molecule traveling at faster than the average speed in the left reservoir approaching the door, it opens the door and lets the fast molecule through to the right reservoir, and then snaps the door shut. Similarly, the demon preferentially allows molecules of slower-than-average speed from the right reservoir to pass into the left one. Over time, heat is steadily transferred from an increasingly cold reservoir to an increasingly hot one, with no net work expended—an apparent violation of the second law of thermodynamics.

The Maxwell’s-demon construct has, over the years, spurred very fruitful discussion in thermodynamics—and also in information theory, where most scientists believe the paradox can be resolved. After more than a century of debate, physicists have generally concluded that the acts of observation, information processing and memory required by the demon bring about an entropy increase within the demon itself, which needs to be considered part of the system’s overall entropy budget. As a result, the second law still holds.

The demon’s quantum side

Researchers at the Moscow Institute of Physics and Technology (MIPT), Russia, ETH Zurich, Switzerland, and the Argonne National Laboratory, USA, now propose extending the concept of Maxwell’s demon to the quantum realm, for the control of qubits, or bits of quantum of information. Their design envisions two ultracold superconducting qubits—fabricated from an aluminum thin film deposited atop a silicon chip—capacitively coupled by one to five meters of coaxial microwave cable, which is cooled to a temperature of a few kelvins. One qubit, the “target” qubit, starts out in a mixed, or impure, quantum state; the other, the “demon” qubit, is in a lower-entropy pure, or superposed, state.

The proposed connection setup, according to the authors, results in an “iSWAP” quantum gate in which, through the exchange of virtual photons, the pure state of the demon qubit is exchanged for the mixed state of the target qubit. Thus the entropy of the energy-isolated target qubit would be reduced, with no change in the qubit’s energy state. While the setup seems locally to violate the second law, information theory once again comes to the rescue: Because the quantum demon needs to initialize its qubit before each interaction, entropy increases on a global level.

The team’s calculations suggest that, if the transmission cable operates at a temperature of a few kelvins, the entropy exchange can take place across one to five meters. That’s a distance that “is huge for quantum mechanics,” as noted by the paper’s lead author, Andrey Lebedev of MIPT and ETH Zurich, in a press release accompanying the work. And, while a temperature in the single kelvin digits might seem frigid, it’s piping hot compared with the superconducting qubits themselves, which must be several orders of magnitude colder.

Computing and nanorefrigeration

While the scheme right now exists mainly on paper, it requires no new technology, and the research team is working on an experimental implementation. Further, though the Maxwell’s-demon construct gives the proposal a decidedly theoretical flavor, the authors see some very practical applications for the work. One such application lies in the realm of quantum computing, where the ability to switch a target qubit’s state from a distance without affecting its energy, using an electromagnetic field, could come in quite handy.

A more exotic application could relate to temperature control. Because the change in the qubit’s entropy could result in a cooling of its immediate environment, coauthor Gordey Lesovik explained in a press release, the system could act as a “nanofridge” that might target very specific, nanoscale parts of molecules. And running the system in reverse would allow it to function as a highly targeted nano-heater as well, according to the scientists.