Volume 21 Issue 10, October 2025

Improvements in qubit performance are essential for the development of large-scale quantum computing devices. Sustained progress requires a broad approach combining physics, materials science, and engineering mindsets.

In this comment, we consider how artificial intelligence tools are reshaping the way mathematical research is conducted and discuss how future developments of this technology will transform mathematical practice.

In our very first issue we published eight research papers, on topics ranging from condensed matter physics to atom interferometry. Two decades on, we look back at those works and hear from their authors.

Topologically protected surface states are expected to exist in topological superconductors. These states have now been detected using momentum-resolved tunnelling spectroscopy in a spin-triplet superconductor.

Like charges can pair up to make superconductors, so intuitively opposite charges should also have no trouble forming pairs. But condensates of electron–hole pairs are not common — one must search carefully for their fingerprints.

Coherent control of magnon excitations is crucial for their potential device application. The integration of the exceptional point in a magnon-photon hybrid system is shown to offer fast, coherent and topologically robust control of magnon-polariton states.

Laboratory measurements reveal that ice exhibits flexoelectricity — the generation of an electrical field upon bending. This flexoelectricity may be the microscopic mechanism for the mysterious charge separation that creates lightning in thunderstorms.

High-purity quantum states, essential for quantum technological applications, were achieved by cooling optically levitated silica nanoparticles.

Imaging through opaque media is challenging. But through the chaos it is possible to discern unique fingerprints of the objects hidden within.

Haptotaxis — a mechanism of sensing adhesive gradients by motile cells — was thought to rely on complex mechanochemistry. It turns out that this mechanism is simply based on the difference of adhesive friction at cell front and rear.

Radiotherapy with charged particles is highly sensitive to uncertainties in their range. Now, radioactive ion beams offer increased precision and real-time imaging for tumour control while maintaining low toxicity to organs at risk.

The most commonly pursued quantum error-correction schemes encode quantum information using multiple two-level qubits. Now, two logical qubits have been encoded in the infinite-dimensional bosonic motional degrees of freedom of a trapped ion.

Experiments that probe the spontaneously broken symmetries in rare-earth tritellurides have revealed a previously hidden ferroaxial density wave arising from intertwined charge and orbital order, which is observed to produce the axial Higgs mode.

Phonons are quanta of the vibrations of the lattice in solids. They can carry angular momentum and allow an emergent chirality. This Perspective defines various types of chiral phonon and classifies the previously observed manifestations of them.

Studies of Bloch oscillations in many-body systems remain limited due to their interaction-induced damping. Now, such oscillations have been observed in a solitonic wave packet of atoms in a Bose gas at the mesoscopic scale.

In strongly correlated systems, how magnetic excitations are renormalized by charge carriers remains an open question. An experiment now reports the observation of magnon-polarons—magnons dressed by doped holes—in a Fermi–Hubbard quantum simulator.

UTe₂ is a proposed intrinsic topological superconductor, but its quasiparticle surface band has not yet been visualized. Now this is achieved using quasiparticle interference imaging, revealing the symmetry of the superconducting order parameter.

Condensates of excitons have been observed in the quantum Hall regime, but evidence for their existence at low magnetic fields remains controversial. Now evidence of coherence between optically pumped interlayer excitons in MoS₂ marks a step towards confirming exciton condensation at low magnetic fields.

Deterministic control of the gain–loss balance in non-Hermitian systems remains challenging. A magnonic hybrid platform is now shown to enable this and, hence, coherently control excitations by leveraging an exceptional point.

The axial Higgs mode is theoretically attributed to a hidden ferroaxial component of charge order. In rare-earth tritellurides, this ferroaxial order is now shown to be induced by intertwined orbital and charge orders.

Ice is not piezoelectric, despite the polarity of water molecules, but bending ice may produce electricity. This has now been experimentally demonstrated, with a flexoelectric coefficient comparable to that of common ceramic materials.

Controlling nanoscale colloidal crystallization is not straightforward. Such control is now achieved by leveraging a metastable liquid phase of charged nanocrystals.

Observing quantum effects in a mechanical oscillator requires it to be close to a pure quantum state, rather than a thermal mixture. Here a librational mode of a levitated nanoparticle is cooled close to its ground state without using cryogenics.

Imaging through complex media is challenging because scattering results in image blurring. By introducing a fingerprint operator and applying it to the measured reflection matrix, information on a target within a complex medium becomes accessible.

Beyond its known role in stabilizing microtubules, it is now shown that tau protein actively promotes lattice defect repair by enhancing tubulin turnover at topological defects.

Imposing shear flow on a cell layer induces an ordering transition. Now it is shown that an intermediate phase of ordering occurs driven by an interplay between cellular activity and the aligning field.

Haptotaxis was traditionally seen as migration up protein gradients. It is now shown that cells can also oscillate or migrate down the gradient.

Particle therapy is subject to uncertainties in the range of the beam. In this study, tumours in the necks of mice were treated with radioactive ion beams, which enabled real-time verification of the beam range.

Quantum spin chains can be represented in several ways, and eigenstates in these dual models have different entanglement structures. By characterizing the dual theories, the optimal tensor network algorithm for simulating the models has been found.

There are many quantum systems that act as high-quality quantum harmonic oscillators, and they can be used to store quantum information using the Gottesman–Kitaev–Preskill code. Entangling gates have now been demonstrated between two of these qubits.

Quantum information cannot be copied, posing challenges for long-distance communication due to signal losses. Here the quantum relay architecture using a single-photon source enhances the signal-to-noise ratio of quantum information transmission.

Names of measurement units often honour notable scientists and are seemingly immune to change. Richard Brown and Juris Meija explore the legacy of this tradition.