The superconducting quantum machine at the centre of a new preprint produced a TUR ratio of 1.71 plus or minus 0.17 at a cold-bath temperature of 81 mK. That is below the classical benchmark of 2, and the authors report it as an experimental violation of the steady-state thermodynamic uncertainty relation.
The TUR is a way of comparing the precision of a steady flow with the entropy produced to maintain it. Here, Q is the ratio being tested, and the canonical classical benchmark says it should be at least 2. A value below that mark is therefore a sub-classical result for the measured circuit, not a claim about every quantum thermal machine.
The machine behind the measurement
The device was an artificial molecule made from two strongly coupled, flux-tunable transmon qubits. Its base measurements were taken below 10 mK unless otherwise specified, while the result compared cold-bath settings of 31 mK and 81 mK.
To create a controlled nonequilibrium flow, the researchers combined a coherent drive with filtered broadband classical flux noise near the splitting between two relevant states. The protocol set equal-rate transitions between those states, while the symmetric state decayed by emitting photons into a microwave waveguide.
Reading the microwave output
The team alternated heterodyne measurements with the operating sequence on and off, using the OFF state as a background reference. From those microwave power records, it estimated the mean photon current and a diffusion coefficient, which describes photon-current fluctuations, over an integration time of 3 microseconds. The fluctuations were inferred from the heterodyne signal rather than from direct counting of individual photons.
Those measured transport quantities agreed well with full-counting-statistics predictions generated from independently characterized device parameters, with no adjustable parameters. The noise-induced mixing rate was calibrated separately from the transport and model analyses by measuring the decay of Rabi oscillations.
Temperature changed the answer
Temperature was central to the result. The extracted ratio remained above the classical threshold at 31 mK, then changed substantially as the cold bath was raised and reached the reported minimum at 81 mK.
The reported plus-or-minus 0.17 uncertainty on the minimum combined sampling variation from repeated measurements with propagated uncertainty in power calibration and cold-bath temperature. Sampling uncertainty accounted for most of the total, and the figure error bars represent two standard deviations.
What the model adds
The model points to a wider operating range than the two tested temperatures alone. Under the experimental drive and dephasing conditions, it predicts an enhancement from approximately 60 mK to 180 mK. That interval is a theoretical prediction, not a complete experimental temperature map.
The analysis also tested the effect of a loss channel that was not independently resolved. Including an unresolved symmetric-mode loss rate of 30 kHz changed the predicted minimum from 1.73 to 1.75. The authors report that the predicted violation remains robust, but this check is a model sensitivity analysis rather than a direct measurement of that channel.
Why the result is still provisional
The work remains a preprint: the supplied document is arXiv version 1, dated 29 September 2026. The central finding is therefore a laboratory report of a sub-classical output ratio, supported by agreement between measured transport data and the model, rather than a demonstrated device application.
It also does not show that the classical relation is violated by all quantum thermal machines, or that the circuit has delivered higher thermodynamic efficiency or a working autonomous quantum clock. Those remain possible directions discussed around the result, while the reported measurement is limited to the output of this superconducting circuit and fluctuations inferred from heterodyne data.
Paper data and sources
Original title: A quantum thermal machine surpassing the classical thermodynamic limit on precision
Authors: Simon Sundelin, Ludvig Nordqvist, Khalak Mahadeviya et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-29
DOI: Not available
Original paper · Full text