Physicists Run the First Cyclic Quantum Heat Engine on a Superconducting Chip

Researchers at VTT Technical Research Centre of Finland and the QTF Center of Excellence have completed three full quantum Otto cycles inside a superconducting circuit, using one tunable junction as both the hot and cold reservoir and pulling a small but positive amount of work out of a qubit.

One Junction Now Plays Both Hot and Cold Reservoir

Heat engines convert a flow of heat into usable work, and physicists have spent two decades asking whether the same trick works inside individual quantum systems. According to the paper, quantum heat engines have already been built from trapped ions, nitrogen-vacancy centers in diamond, and cold atoms, but no one had run a complete, repeating cycle inside a superconducting circuit until now.

The team's sample pairs a flux-tunable transmon qubit, the working medium, with a single-junction quantum-circuit refrigerator, or QCR, standing in for both thermal reservoirs. The transmon's lowest transition sits at 4.047 GHz with an anharmonicity of -279 MHz, and the QCR is a normal-metal-insulator-superconductor junction with a measured superconducting gap of 186 microelectronvolts and a tunneling resistance of 25.7 kiloohms. A capacitively coupled auxiliary resonator at 4.670 GHz links the qubit to the QCR, a separate readout resonator at 7.436 GHz handles dispersive state measurement, and the Dynes parameter describing the density of subgap states in the junction was measured at 4.0 x 10⁻³.

Biasing that single junction with different voltages lets it act as either a cold sink or a hot source, so the same physical part supplies both reservoirs a classical Otto engine would need as separate hardware. Between the QCR pulses, trapezoidal current pulses through the qubit's flux line raise and lower its transition frequency, doing the mechanical work of the cycle. Four strokes make up one pass: an adiabatic expansion, an isochoric cooling stroke driven by a cold-biased QCR, an adiabatic compression, and an isochoric heating stroke driven by a hot-biased QCR, shown below with the durations used in the experiment.

Three Cycles, Measured Stroke by Stroke

The team started the qubit in its unbiased thermal state, fit at an effective temperature of 160 millikelvin, and ran three consecutive Otto cycles while reading out the qubit's population in every state with 10,000 single shots per data point and a four-component Gaussian mixture model. A Lindblad master-equation simulation, run with the same pulse parameters, tracked closely with what the single-shot readout measured.

The cycle did not close cleanly. Because the heating stroke pulled in more energy than the cooling stroke removed at low starting temperature, the qubit's effective temperature climbed from around 200 millikelvin to around 600 millikelvin over the three measured cycles instead of returning to its starting point. A longer simulated run shows why: the state saturates near 600 millikelvin after about five cycles, with a fitted saturation time constant of 1.0 microsecond, so the three-cycle experiment captured the transient climb rather than the steady operating point.

The Efficiency Gap Between Otto's Ideal and What the Chip Delivers

Repeating the first cycle eight times let the team compute the engine's output power and efficiency directly from the measured populations and transition frequencies. The mean output power came out to 0.039 electronvolts per second, with the mean efficiency at 0.55 percent, both matching simulated values of 0.031 electronvolts per second and 0.45 percent within their reported uncertainties, which stayed below 5 percent across repetitions. The authors also checked whether the engine's output fluctuates more than expected for a device this small, noting that a full trajectory-level test of thermodynamic uncertainty relations was outside the scope of this work; across repeated cycles, the measured power and efficiency varied only modestly around their mean values.

Every quantum Otto engine has a hard ceiling set by its own compression ratio, the ratio between the qubit's highest and lowest transition frequency during the cycle. For the -82.4 megahertz detuning used here, that ceiling works out to 2.0 percent, and the measured 0.55 percent efficiency is about 27 percent of it, a gap the authors attribute to the first cycle running far from thermal saturation rather than to any flaw in the pulse sequence. Their simulations put the steady-state efficiency, once the cycle saturates, at 2.2 percent, essentially matching the theoretical Otto limit.

None of these four numbers is close to what a heat engine could theoretically extract from these two reservoirs. Estimating reservoir temperatures from long heating and cooling pulses puts the Carnot limit, the absolute ceiling set by thermodynamics rather than by this particular cycle, at around 83 percent. Prior quantum heat engines built from single ions and atomic collisions have reported efficiencies of 42 to 48 percent, though those platforms also fall well short of their own Otto limits; they operate with far higher compression ratios than a single transmon's finite frequency range allows, which is why they land so much closer to their ceiling than this device does to its own.

What This Demonstration Does and Doesn't Prove

The paper is explicit about scope. The authors describe the result as an initial demonstration whose power and efficiency currently lack practical application, and they note the cycle is not perfectly closed since the qubit's mean energy at the start and end of each pass does not exactly match. Only three cycles were measured at high resolution because of measurement-time and data-volume limits; steady-state operation appears only in the simulation, not in the recorded data.

Superconducting circuits have handled one-way thermal control for years. Researchers have already shown a quantum-circuit refrigerator acting as a thermally driven quantum refrigerator that resets a qubit, and a separate group reported a non-cyclic thermal machine claiming to reach the heat-engine regime with superconducting hardware in a related demonstration published earlier in 2026. What distinguishes this result is the closed, repeating cycle: the same junction switching between hot and cold, on a schedule, over multiple passes, with the qubit's state tracked at every stroke. The sample itself was built with the group's standard toolkit: a niobium ground plane and resonators on silicon, aluminum Josephson junctions for the transmon's SQUID loop, and a copper-based junction for the QCR, deposited with a thin aluminum adhesion layer to keep the copper from turning superconducting.

The efficiency numbers will need to climb by more than an order of magnitude before a device like this does anything useful on its own. But as quantum hardware moves from single demonstrations toward reusable, standardized building blocks for larger systems, a heat engine built on the same superconducting fabrication process as a qubit processor is one more piece of thermal-management infrastructure a future quantum computer might eventually draw on, alongside the resets and refrigerators already demonstrated on the same chip platform.