March 19, 2026 -- Physicists have mixed feelings about nonlinearity. They may explore nonlinear behaviours with calculations and simulations, but in the laboratory they often like to keep things as linear as possible – for instance, by limiting the strength of the excitations to which the systems they study respond. Over the past three decades, researchers in quantum information science have developed methods and techniques to control and manipulate quantum systems in low-excitation regimes where nonlinearities are negligible: this successful approach led to many promising advances in platforms such as trapped ions and superconducting circuits. To perform ever faster quantum operations with increasingly higher fidelities, however, there's a growing consensus in the community that the time has come to find out how to take advantage of nonlinearities.

In a paper recently published in Physical Review X, joint first authors Ivan Rojkov – now a postdoctoral fellow at the Yale Quantum Institute at Yale University in the US – and Matteo Simoni, together with colleagues in the D-PHYS group of Professor Jonathan Home and at the Fraunhofer Institute for Applied Solid State Physics in Germany, present a theoretical framework that reads like an invitation to view nonlinearity as an ally.

The researchers introduce a general approach for stabilising quantum states through interfering nonlinear processes in an engineered dissipation mechanism that is coupled to a quantum system. In this context, stabilisation refers to the operation through which the state of a physical system remains close to a desired target state even in the presence of disturbances such as decoherence. The authors call their method nonlinear reservoir engineering, a name stressing the close connection with the previously established techniques for engineering dissipation that already proved highly valuable for quantum error correction.

Engineering the reservoir

The idea that one could "design" the coupling between a quantum system and a surrounding environment to realise specific control operations on the system surfaced in the late nineties: the theoretical proposal considered a harmonic oscillator, such as a single trapped ion, coupled to a reservoir of oscillators, for example the vacuum modes of the electromagnetic field, with an external laser field acting as the knob for producing the desired coupling. The original proposal didn't mention quantum state stabilisation or quantum error correction; the connection to these applications becomes even more apparent, however, when the environment to which the quantum system is coupled is a bath that can remove entropy.

A single trapped ion is a prime example of a bosonic harmonic oscillator: it was with this system that the first experimental demonstrations of reservoir engineering were achieved, showing how the system could be stabilised in a range of states including squeezed and entangled states. Those experiments opened the way to the stabilisation of so-called bosonic error correction codes. In these codes, computational errors can be corrected thanks to the redundant encoding of quantum information unlocked by the infinite-dimensionality of the Hilbert space describing a quantum harmonic oscillator.

Stabilising cat states

A notable bosonic code is based on one of quantum physics' most famous quantum resources and its extensions: a Schrödinger's cat state, namely the two-component superposition of displaced coherent states of a quantum harmonic oscillator. If the superposition involves not only two but four coherent states, the associated bosonic code is known as a four-legged cat code – and so on.

Stabilising two-legged cat codes was successfully demonstrated with superconducting circuits, but multi-legged cat code stabilisation has remained challenging. With trapped ions, even stabilising two-legged cat codes was deemed extremely difficult. According to Rojkov, Simoni and colleagues, the bottleneck lies precisely the requirement for a low-excitation regime in the original reservoir engineering theory. This is why the team decided to walk away from the linear approximation, turning the nonlinearity of ion-light interactions to their favour to achieve quantum state stabilisation.

In the paper, the researchers consider a bosonic harmonic oscillator coupled to a damped system described by a bosonic operator that comprises boson raising and lowering nonlinear processes, that is, terms responsible for boson gain and loss. What the authors show is that it's possible to engineer the strengths of these two processes so that they interfere destructively, leading to stabilised multi-legged cat states.

What are the error correction capabilities of nonlinearly stabilised cat states? Rojkov, Simoni and coworkers found that the very nonlinearity that characterises their approach can improve both the strength of state stabilisation and the corrective properties of cat codes. In the paper, they discuss the applicability of the nonlinear reservoir engineering method to trapped ions and superconducting circuits. As the nonlinearities they consider also characterise other quantum systems, such as spin ensembles and optomechanical systems, the authors believe their method to be widely transferrable.

In fact, a very recent experimental demonstration performed in the Home group has showed successful multi-legged cat code stabilisation with a single trapped ion. The published theoretical work and its companion experimental realisation, for which a manuscript is presently under peer review, thus lend strong support to the potential of this new approach for advanced quantum control.