Programming anharmonic potentials in a superconducting harmonic oscillator

In the quantum world, the most fundamental building blocks of matter often behave like perfect springs. When an atom vibrates or a molecule wiggles, it frequently follows a simple, predictable rhythm known as a harmonic oscillation. This behavior is so reliable that scientists have built entire quantum computers around it, using these vibrating systems as a stable foundation for processing information. However, the real universe is rarely so simple. Chemical reactions, the way molecules break apart, and the complex interactions that drive life itself are governed by forces that do not follow a perfect spring. These forces are "anharmonic," meaning they change their behavior depending on how far you stretch or compress them. To simulate these real-world processes on a quantum computer, researchers need to be able to create these complex, non-linear forces on demand. Until now, engineering such specific, custom-made forces has been a significant hurdle, often requiring unique hardware for every single new task.

A team of researchers has now demonstrated a flexible method to program these complex forces directly into a superconducting quantum device. They worked with a quantum harmonic oscillator, a device that naturally vibrates like a perfect spring, and connected it to a tiny artificial atom called a transmon qubit. By carefully controlling the interaction between the two, they created a system capable of acting like a universal tool for shaping quantum forces. Instead of building a new machine for every new type of vibration they wanted to study, they developed a single, reconfigurable circuit. This circuit works by interleaving rapid rotations of the artificial atom with precise shifts of the oscillator's position. By simply changing the angles of the rotations, the researchers could program the device to mimic a wide variety of complex potentials, effectively telling the oscillator to behave as if it were trapped in a custom-designed energy landscape.

The team first tested their method by creating a cubic phase gate, a specific type of force that is essential for performing universal quantum computations. They programmed the device to apply a force that grows stronger the further the oscillator moves from its center, a behavior that is impossible for a standard spring. To verify that they had succeeded, they used a technique called pointwise force reconstruction. They sent a series of gentle, well-defined probes through the system and measured how much the momentum of the oscillator changed. By mapping these changes, they were able to reconstruct the shape of the force the device had applied. The results showed that the device successfully created the intended cubic shape, with the measured force matching the programmed target within a very small margin of error. The quantum states produced by this gate were highly complex and non-standard, confirming that the device had successfully generated the necessary non-Gaussian resources required for advanced quantum information processing.

Building on this success, the researchers engineered a family of double-well potentials. These are energy landscapes that look like a valley with two dips separated by a hill, a shape that is crucial for understanding how particles tunnel through barriers or how chemical bonds break and reform. They programmed the device to create a perfectly symmetrical double well, where both dips were identical, and then modified the settings to create an asymmetrical version where one dip was deeper than the other. They also created a "broken" version where the hill disappeared entirely, leaving only a single slope. In each case, the reconstruction of the force profile clearly showed the intended shape. For the symmetrical version, the force was perfectly balanced; for the asymmetrical one, the balance was shifted exactly as programmed; and for the broken version, the characteristic double-dip structure vanished. This demonstrated that the system could not only create complex shapes but could also be tuned with high precision to alter the symmetry of those shapes.

Finally, the team tackled one of the most challenging targets: the Morse potential. This is a specific type of force that describes how atoms in a molecule vibrate and eventually separate, characterized by a steep wall on one side and a gentle, flattening slope on the other. This shape is fundamentally different from the polynomial shapes they had created before, as it involves an exponential curve. The researchers programmed the device to approximate this potential. While the reconstruction showed the general shape, the steep, sharp wall of the Morse potential was not fully resolved. The researchers identified that this limitation was not due to a flaw in their programming, but rather a consequence of the measurement method itself. The probes they used had a finite width, which smoothed out the sharpest details of the force, much like how a slightly blurry lens cannot capture the finest edge of a photograph.

Through simulations, the team showed that if they used a different type of probe—one that was squeezed to be much narrower in position—the sharp wall of the Morse potential would be recovered with high fidelity. This finding provided a clear path forward: the hardware is capable of the task, and the remaining limitation is simply a matter of using a more precise measurement tool, which is already available in similar experimental setups. The work establishes a practical and reconfigurable route to programming anharmonic potentials. By varying only a set of rotation angles, the researchers can switch between creating cubic forces, double-well traps, and molecular vibration models on the same piece of hardware. This capability opens the door to simulating complex molecular dynamics and chemical reactions with a level of detail that was previously out of reach, moving quantum simulation closer to the reality of the physical world.