María José Martinez Perez

In 2025, the Year of Quantum Science and Technology ( https://quantum2025.org/ ), we celebrate a century of quantum mechanics, witnessing a surge in activities that illuminate its inherent strangeness and drive technological innovation. Superconductivity, discovered 114 years ago, stands as a prime example, offering direct and compelling evidence of macroscopic quantum phenomena. Beyond its ability to conduct immense currents without loss, superconductivity reveals the quantum realm operating on a scale we can directly observe and manipulate. The macroscopic quantum coherence, where an ensemble of particles is described by a single wave function, leads to remarkable consequences: dissipation-less current and flux quantization—the basic properties exploited in superconducting quantum circuit fabrication. This Roadmap has been inspired by intensive discussions and collaborations emerging from the European Cooperation in Science & Technology COST-Action CA21144 (SuperQuMap—Superconducting Nanodevices and Quantum Materials for Coherent Manipulation). The aim of the COST Action SuperQuMap is to establish a strong European network centered on macroscopic quantum behavior in superconductors, bringing together groups of different backgrounds and more than 30 countries. The roadmap outlines the network’s concrete activities, driving advancements in superconductor-based quantum technologies and charting future directions. Spanning fundamental research to practical applications, the roadmap incorporates insights from industry partners developing quantum computation. It begins by exploring quantum materials, highlighting how topology and electronic correlations could catalyze a quantum leap in technology. We then delve into manipulating the superconducting phase, leveraging advancements in magnetism, 3D fabrication, and tunable correlations. Further, we showcase the advanced microscopy techniques—such as angle-resolved photoemission spectroscopy and scanning probes—used to visualize quantum behavior. Finally, and crucially, we detail the quantum devices developed within the network, and their transformative impact on modern quantum computing approaches.

Quantum technologies require platforms that can coherently interface qubits with bosonic excitations. Photons have traditionally played this role in cavity quantum electrodynamics, but achieving the same goal using solid-state bosons remains challenging. Here we demonstrate strong and tunable spin-magnon coupling between molecular spin qubits and magnons in a van der Waals antiferromagnetic insulator. Using [Gd(W$_5$O$_{18}$)$_{2}$]$^{9-}$ as the spin ensemble and CrSBr as the magnonic resonator, we observe anticrossings and coherent hybridization, realizing magnon quantum electrodynamics for the first time. Crucially, by rotating the magnetic field, we can dynamically change the magnon symmetry from linear to chiral, enabling in-situ tuning of the coupling strength. Our results establish magnonic cavities as a platform for scalable chiral quantum optics with magnetic materials.

Magnetic vortices are relevant in fields like biomedicine, data storage, and quantum technologies. For quantum applications, it is crucial to have nanoparticles free from metastable configurations and with narrow switching field distributions, especially at very low temperatures, where vortex nucleation and annihilation have rarely been studied. This work shows that these properties are strongly influenced by the shape of the nanoparticle, with an even greater impact at low temperatures. To investigate this, high‐transition‐temperature nanoscopic Superconducting Quantum Interference Devices are used to detect the magnetization of individual permalloy nanodiscs that host a magnetic vortex. Both the sensors and the nanodiscs are fabricated using focused ion beam milling, and each nanodisc is carefully attached to the sensor using a micromanipulator inside a dual‐beam microscope. The measurements allow to explore the complex energy landscape that governs vortex nucleation and annihilation at the nanoscale, particularly at low temperatures. This study quantifies how likely it is for the system to get trapped in metastable states and shows that this can be minimized by carefully controlling the nanoparticle's shape during fabrication. This study's data thus illustrate how ion beam nanofabrication enables precise control over nanoparticle morphology, with significant implications for their performance.

The controlled integration of magnetic molecules into superconducting circuits is key for developing hybrid quantum devices. Here, we study [Dy₂] molecular dimers deposited onto micro-SQUID susceptometers. The results of magnetic, heat capacity and magnetic resonance experiments, backed by theoretical calculations, show that each [Dy₂] dimer fulfills the main requisites to encode a two-spin quantum processor. Arrays of between 2×10⁸ to 7×10⁹ [Dy₂] molecules have been optimally integrated, under ambient conditions, inside the 20 μm wide loops of micro-SQUID sensors by means of Dip-Pen Nanolithography. The equilibrium magnetic susceptibility and the phonon-assisted spin tunneling dynamics measured in situ evidence that these molecules preserve the spin ground states, magnetic interactions and magnetic asymmetry that characterize them in bulk. These results show that it is possible to interface multi-qubit molecular complexes with on-chip superconducting circuits without disturbing their relevant properties and hints at the potential of soft nanolithography techniques to achieve this goal.

We present an extension of the well-known micromagnetic package Mumax3 to simulate magnon-polaritons in realistic magnetic materials and nanostructures. Mumax3-cQED leverages the full GPU-accelerated capabilities of Mumax3 to model standard spin-spin interactions and the coupling of magnetic moments to external space- and time-dependent magnetic fields, with the additional unique feature of including the coupling to a cavity. We validate the code against results obtained from the Dicke model in both the paramagnetic and the superradiant phases. We show that hybrid magnon-light states can be calculated, as well as the non-equilibrium dynamics and their approach to equilibrium. In addition, we demonstrate the potential of Mumax3-cQED to reproduce experimental results and design magnon-cavity experiments, including three-dimensional and coplanar waveguide resonators. The code is fully available and will be useful for designing experiments involving microscopic saturated ferromagnets as well as systems featuring spin textures such as domain walls, vortices, or skyrmions.

Performing nanoscale scanning electron paramagnetic resonance (EPR) requires three essential ingredients: First, a static magnetic field together with field gradients to Zeeman split the electronic energy levels with spatial resolution; second, a radio frequency (rf) magnetic field capable of inducing spin transitions; finally, a sensitive detection method to quantify the energy absorbed by spins. This is usually achieved by combining externally applied magnetic fields with inductive coils or cavities, fluorescent defects, or scanning probes. Here, we theoretically propose the realization of an EPR scanning sensor merging all three characteristics into a single device: the vortex core stabilized in ferromagnetic thin-film discs. On one hand, the vortex ground state generates a significant static magnetic field and field gradients. On the other hand, the precessional motion of the vortex core around its equilibrium position produces a circularly polarized oscillating magnetic field, which is enough to produce spin transitions. Finally, the spin-magnon coupling broadens the vortex gyrotropic frequency, suggesting a direct measure of the presence of unpaired electrons. Moreover, the vortex core can be displaced by simply using external magnetic fields of a few mT, enabling EPR scanning microscopy with large spatial resolution. Our numerical simulations show that, by using low damping magnets, it is theoretically possible to detect single spins located on the disc's surface. Vortex nanocavities could also attain strong coupling to individual spin molecular qubits with potential applications to mediate qubit-qubit interactions or to implement qubit readout protocols.

Performing nanoscale scanning electron paramagnetic resonance (EPR) requires three essential ingredients. First, a static magnetic field together to field gradients to Zeeman split the electronic energy levels with spatial resolution. Second, a radiofrequency (rf) magnetic field capable of inducing spin transitions. Finally, a sensitive detection method to quantify the energy absorbed by spins. This is usually achieved by combining externally applied magnetic fields with inductive coils or cavities, fluorescent defects or scanning probes. Here, we theoretically propose the realization of a EPR scanning sensor merging all three characteristics into a single device: the vortex core stabilized in ferromagnetic thin-film discs. On one hand, the vortex ground state generates a significant static magnetic field and field gradients. On the other hand, the precessional motion of the vortex core around its equilibrium position produces a circularly polarized oscillating magnetic field, which is enough to produce spin transitions. Finally, the spin-magnon coupling broadens the vortex gyrotropic frequency, suggesting a direct measure of the presence of unpaired electrons. Moreover, the vortex core can be displaced by simply using external magnetic fields of a few mT, enabling EPR scanning microscopy with large spatial resolution. Our numerical simulations show that, by using low damping magnets, it is theoretically possible to detect single spins located on the disc's surface. Vortex nanocavities could also attain strong coupling to individual spin molecular qubits, with potential applications to mediate qubit-qubit interactions or to implement qubit readout protocols.

A quantum spin liquid (QSL) is an elusive state of matter characterized by the absence of long-range magnetic order, even at zero temperature, and by the presence of exotic quasiparticle excitations.