Superconducting Qubits

That author's affiliation: Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, Madrid, Spain Institution (first & last author): University of Grenoble Alpes, CEA, Grenoble INP, IRIG-Pheliqs, Grenoble, France

Coupling semiconductor qubit devices to microwave resonators provides a way to transfer quantum information over long distances. A flopping-mode qubit that combines strong coupling to photons with good coherence properties has now been demonstrated.

Higher-order interactions in quantum harmonic oscillator systems can result in useful effects, but they are hard to engineer. An experiment on a single trapped ion now demonstrates how spin can mediate higher-order nonlinear bosonic interactions.

That author's affiliation: Radboud University Institution (first & last author): Max Planck Institute for Structure and Dynamics of Matter

The superconducting diode effect (SDE) allows polarity-dependent critical currents when time-reversal and current-inverting spatial symmetries are broken. Superconducting diodes show promise for applications, but inversion asymmetry is usually encoded in sample geometry or non-centrosymmetric crystals, rendering them static circuit elements. Here we demonstrate a programmable superconducting diode whose functionality is encoded in correlated electronic domains. We use the nematic superconductor FeSe as a platform and report a large intrinsic SDE with efficiencies up to $\eta \sim 75\%$ due to vortices interacting with nematic twin boundaries. The domain wall configuration thus encodes the SDE of the device. Through intense microsecond current pulses to quench the nematic order at rates exceeding $10^7$~K/s, we modify the domain pattern and control the polarity and strength of the SDE. These results establish a new paradigm in which superconducting circuit elements can be programmed through patterns imprinted into correlated electronic states.

That author's affiliation: IFW Dresden First author institution: IFW Dresden Last author institution: University of Salerno, Italy

Ten years after the experimental discovery of Weyl semimetals, theoretical and experimental work has pointed to the possibility of realizing surface-only superconductivity at relatively high temperatures in these materials. A consensus is developing that this unusual form of superconductivity is mediated by surface electronic states unique to Weyl semimetals, known as Fermi arcs. In this work, we show that the topological protection of these exotic states can be exploited to engineer high critical temperatures. Motivated by a real-material example (PtBi$_2$), we demonstrate that surface van Hove singularities can be induced by depositing a suitable additional layer on top of the Weyl surface. We also investigate the role of these singularities in raising the critical temperature, showing that it is significantly enhanced when the chemical potential lies in their vicinity. More generally, our results demonstrate how topological protection can be exploited to manipulate surface electronic states, thereby opening experimentally accessible routes toward engineering high-temperature two-dimensional superconductivity and other exotic phases.

That author's affiliation: University of Perugia First author institution: University of Perugia Last author institution: Unknown

Bose metals are metals made of Cooper pairs, which form at very low temperatures in superconducting films and Josephson junction arrays as an intermediate phase between superconductivity and superinsulation. We predicted the existence of this 2D metallic phase of bosons in the mid 90s, showing that they arise due to topological quantum effects. The observation of Bose metals in perfectly regular Josephson junction arrays fully confirms our original prediction and rules out alternative models based on disorder. Here, we review the basic mechanism leading to Bose metals. The key points are that the relevant vortices in granular superconductors are core-less, mobile XY vortices which can tunnel through the system due to quantum phase slips, that there is no charge-phase commutation relation preventing such vortices to be simultaneously out of condensate with charges, and that out-of-condensate charges and vortices are subject to topological mutual statistics interactions, a quantum effect that dominates at low temperatures. These repulsive mutual statistics interactions are sufficient to increase the energy of the Cooper pairs and lift them out of condensate. The result is a topological ground state in which charge conduction along edges and vortex movement across them organize themselves so as to generate the observed metallic saturation at low temperatures. This state is known today as a bosonic topological insulator.

That author's affiliation: Institute of Physics, Chinese Academy of Sciences First author institution: Unknown Last author institution: Institute of Physics, Chinese Academy of Sciences

The chromium-based kagome metal CsCr3Sb5 has garnered significant interest due to its strong electron correlations, intertwined orders and potential for unconventional superconductivity under high pressure. The evolution of magnetic and superconducting interactions as the more frequently studied CsV3Sb5 is doped to CsCr3Sb5 remains poorly understood. Here, we demonstrate the emergence of a spatially anisotropic Kondo resonance intertwined with the superconducting gap, enabled by introducing magnetic Cr impurities into the kagome superconductor CsV3Sb5. The addition of dilute Cr impurities not only weakens long range charge density wave order but also produces local magnetic moments that leads to Kondo resonances. We show that the Kondo resonance forms anisotropic, ripple like spatial patterns around individual Cr atoms, breaking all local mirror symmetries. We further reveal that with the emergence of Kondo screening, the coherence peak and depth of superconducting gap with finite zero-energy conductance are enhanced. This suggests that non superconducting carriers at the Fermi surface in the parent compound participate in the Kondo effect, simultaneously screening Cr magnetic moments and increasing the superfluid density. Our findings offer an opportunity to study the interplay between superconductivity and local magnetism in kagome materials.

That author's affiliation: QuTech Institution (first & last author): University of Wisconsin–Madison

Orbital energy splittings are important quantum dot parameters for the operation of hole spin qubits. They are known to depend on the lateral confinement of the quantum dots. However, when changing top, plunger gate voltages, which are the typical control parameter for qubit applications, such energy splitting changes are typically negligible, both as measured in experiment and as assumed in effective theories. Here, we study the singlet-triplet (ST) splittings, which depend on the orbital splittings, of a double quantum dot (DQD) in a Ge/SiGe heterostructure using photon-assisted tunneling (PAT) and pulsed-gate spectroscopy. We find that the ST splittings have a surprising, strong dependence on the top gate voltages, leading to anomalous PAT measurements. We combine data from both measurements in a model that well describes the linear gate-voltage dependence of the ST splittings. Finally, we show that the ST splittings of the two dots exhibit similar linear gate-voltage dependences when the device is retuned such that their ratio is significantly different.

That author's affiliation: The University of Hong Kong First author institution: Unknown Last author institution: The University of Hong Kong

Fractional quantum anomalous Hall (FQAH) effect, a lattice analogue of fractional quantum Hall effect, offers a unique pathway toward fault-tolerant quantum computation and deep insights into the interplay of topology and strong correlations. The exploration has been successfully guided by the paradigm of ideal flat Chern bands, which mimic Landau levels in both band topology and local quantum geometry. Yet, given the boundless potential for Bloch bands in lattice systems, it remains a significant open question whether FQAH states can arise in scenarios fundamentally distinct from this paradigm. Here we turn to a class of gapless flat bands, featuring (i) ill-defined band topology, (ii) non-quantized Berry flux, (iii) divergent quantum geometry at singular band touchings, (iv) highly fluctuating and far-from-ideal quantum geometry across the Brillouin zone (BZ). Our exact diagonalization and density matrix renormalization group calculations unambiguously demonstrate FQAH phase that is virtually independent of the interaction strength, persisting from the weak-interaction to the strong-interaction limit. We find the stability of the FQAH states does not uniquely correlate with the singularity strength or the BZ-averaged quantum geometric fluctuations. Instead, the many-body topological order can adapt to the singular and fluctuating quantum geometric landscape by spontaneously developing an inhomogeneous carrier distribution, while its quenching accompanies the drop in the occupation-weighted Berry flux. Our work reveals a profound interplay between local quantum geometry and many-body correlation, and significantly expands the exploration space for FQAH effect and correlated phenomena in general.

That author's affiliation: Wuerzburg University First author institution: Unknown Last author institution: Wuerzburg University

We study twisted bilayer WSe$_2$ within a continuum moir\'e model and introduce a method for treating finite geometries directly in the continuum framework, overcoming limitations associated with momentum-space formulations and Wannier obstructions. By projecting a confinement potential onto bulk moir\'e eigenstates, we obtain a real-space description of edge physics without lattice models. Applying this approach to nanoribbons, we demonstrate chiral edge modes consistent with bulk Chern numbers and reveal their moir\'e-scale character. In the magic-angle regime, these states are strongly localized, exhibit layer-polarized counter-propagating modes, and are electrically tunable via a displacement field, enabling control of localization, hybridization, and topological transitions. Our results establish a general framework for boundary physics in topological moir\'e materials.

That author's affiliation: Centre de Nanosciences et de Nanotechnologies First author institution: Unknown Last author institution: Centre de Nanosciences et de Nanotechnologies

Multi-dimensional frequency-bin entanglement-based quantum key distribution network

In the mixed state of type-II bulk superconductors, the magnetic field penetrates in the form of vortices enclosing one magnetic flux quantum: this is the conventional Abrikosov vortex lattice. Here, by using transverse muon-spin spectroscopy, we demonstrate the presence of an unconventional vortex lattice in LiFeAs single crystals. We also show evidence that the new mixed phase consists of stripes of "coreless" vortices, which are bound states of two spatially separated half-quantum vortices.

In a Josephson junction network, anisotropic coupling between spin triplet pairing correlations can lead to frustrated $d$ vector textures that support spontaneous Josephson currents and nonintegral flux trapping. Such networks can appear in superconducting polycrystals, as well as single-crystal superconductors. In analogy to classical spin systems, in which the presence of geometric frustration and anisotropic superexchange can lead to nontrivial spin textures, Josephson networks with anisotropic Josephson couplings cannot simultaneously optimize their $\mathrm{U}(1)$ superconducting phase difference and relative $d$ vector orientations. The internal pairing structure of Cooper pairs twists as they tunnel across the Josephson junction, and the $d$ vector texture enters as an emergent geometric phase which can spontaneously trap fractional flux. For unitary triplet pairing order, this mechanism can support $\pi$-flux trapping above a critical value of antisymmetric Josephson coupling, and is distinct from usual half-quantum vortices. The results of this work reveal new routes to engineer frustrated Josephson networks from the interplay of magnetic textures and spin triplet superconducting pairing order.

Compact scalar field theories on lattices are capable of describing a large class of many-body systems, such as interacting bosons, superconducting circuit networks, spin systems and more. We show that a generic quantum geometric many-body coupling induces quantized Chern couplings, implementing a lattice network version of a Florianini-Jackiw theory. Quantum geometry thus unlocks a direct mapping from scalar fields to anyons with fractional exchange phases, relevant for quantum error correction codes and quantum chemistry computation applications. In contrast to more familiar local Chern-Simons constructions with a uniform level, the compact-phase quantum geometry considered here yields pair-dependent topological couplings that can be nonlocal in node space and are encoded by a nonuniform first-Chern matrix. This feature introduces the notion of non-identical anyons, i.e., excitations that do not mutually satisfy the same exchange statistics. Such non-identical exchange statistics open up a microscopic pathway to a virtually unexplored class of non-local field theories breaking the Wigner superselection rule, allowing to explore non-local communication (all-to-all qubit gates) with local control.

We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting $A$. The BCS scar ground state is a linear combination of the well-known $\eta$-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.

We study quantum tunneling through a potential barrier whose height fluctuates in time and is modeled by Gaussian white noise. We map the stochastic dynamics onto an equivalent time-independent Lindblad equation for the density matrix, allowing fully analytical solutions. For Schr\"odinger particles, noise introduces dissipation that suppresses Fabry-P\'erot oscillations and yields an exponentially decaying transmission. Applying the same formalism to graphene, we demonstrate that noise induces a complex longitudinal wavevector within the barrier, leading to a strong suppression of transmission and Klein tunneling, even at normal incidence. Our approach promises improved control over Klein tunneling. These results demonstrate that noisy barriers can act as tunable dissipative elements, offering a pathway to enhanced control of electron transport in graphene-based devices. We also briefly discuss how our results could guide the design of graphene quantum dots for potential use in spin qubit devices.

That author's affiliation: Delft University of Technology First author institution: The Institute of the Polish Language of the Polish Academy of Sciences Last author institution: RWTH Aachen University

Charge separation from the $(4,0)$ to the $(3,1)$ state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the $(3,1)$ singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of $g$-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.

Gatemon qubits are based on a superconductor-quantum dot-superconductor (S-QD-S) junction which enables in situ electrostatic tuning via a gate electrode. For a single-channel QD this structure gives rise to two subgap Andreev bound states (ABSs), and generally leads to a richer quantum phase dynamics as compared to conventional transmons. In a recent work [Phys. Rev. B 111, 214503 (2025)] we derived the quantum phase dynamics from a many-body treatment which leads to an effective gate voltage-dependent Hamiltonian that self-consistently incorporates the phase quantization. It predicts (i) a renormalization of the junction's effective capacitance and (ii) the presence of gate voltage and occupation-dependent charge offsets in junctions with tunneling asymmetry. Here, we quantify the observable impact of these effects on the qubit's energy spectrum and anharmonicity, by studying the interplay of the two Andreev branches as a function of dot-gate voltages and junction transparencies. We show the relation of these predictions to simplified gatemon models and propose a protocol to experimentally detect the predicted charge offsets.

Semiconductor quantum dots (QDs) offer outstanding quantum-optical properties, making them highly attractive for quantum information technologies. However, combining wide-range electrical tunability, efficient photon extraction, elevated-temperature operation, monolithic silicon integration, and telecom-wavelength compatibility remains a major challenge. Here, we demonstrate electrically contacted circular Bragg grating (eCBG) resonators incorporating InGaAs QDs directly grown on silicon, enabling bright single-photon emission in the telecom O-band. Deterministic electron-beam lithography and a ridge-based vertical p--i--n diode architecture enable precise device integration and electrical control of individual emitters. The QD--eCBGs exhibit a quantum-confined Stark shift of approximately 16 nm (11 meV) at 4 K, representing a record for QDs embedded in nanophotonic structures at telecom wavelengths. This is achieved alongside a photon extraction efficiency of $(21.7 \pm 3.0)\%$ into the first lens, while maintaining excellent radiative properties and high single-photon purity, with $g^{(2)}(0)=0.0078 \pm 0.0012$ below saturation and $g^{(2)}(0)=0.0183 \pm 0.0021$ at saturation under pulsed excitation. Robust antibunching persists up to 77 K, with $g^{(2)}(0)=0.0663 \pm 0.0056$, enabling operation with liquid-nitrogen or compact Stirling cryocoolers. Furthermore, spatially separated QD--eCBGs can be electrically tuned into spectral resonance without degrading photon statistics. These results establish a silicon-compatible, electrically addressable telecom O-band quantum light platform combining wide spectral tunability, high single-photon purity, and elevated-temperature operation, providing a scalable route toward practical photonic quantum networks.

Three-dimensional (3D) topological ferroelectric (FE) insulators, in which topological and FE orders naturally coexist, enable field-controlled spintronic devices. In this work, we predict a new structure of bismuth monohalides Bi4Br4 and Bi4I4, denoted $\gamma$ phase, and demonstrate that it is an ideal 3D topological FE insulator. Systematic first-principles calculations confirm the stability and synthesizability of $\gamma$-Bi4X4 (X=Br, I). Although the noncentrosymmetric $\gamma$ phase crystallizes in the space group $Cmc2_1$ with no symmetry-based classifications/indicators, the nontrivial topology can be characterized by the spin Chern number (SCN). Spin-resolved Wilson loops show the $s_z$ SCN $C_{s_z}=2$, indicating the spin-resolved topology of a 3D quantum spin Hall insulator state. The $z$-direction polarization can be switched by interlayer sliding, requiring only crossing a small energy barrier. Finally, we design an electrically controlled spin-filter device on bilayer films that can generate a switchable spin-polarized current. Combining a single-phase crystal, a sizable band gap, and robust band topology against FE switching, these bismuth monohalides serve as a prototype of intrinsic 3D topological FE insulators, providing an ideal platform for realizing new nonvolatile functionalities in spintronic devices.

That author's affiliation: School of Physics, University of Melbourne, Parkville, Australia First author institution: School of Physics, University of Melbourne, Parkville, Australia Last author institution: School of Physics, University of Melbourne, Parkville, Australia, Australian Research Council Centre for Quantum Computation and Communication Technology

Magnetic clock transitions (CTs), defined by vanishing first-order sensitivity of the transition frequency to magnetic field fluctuations, provide a powerful route to suppress decoherence in donor spin systems. Here, we present the observation of magnetic field CTs from an ensemble of near-surface $^{75}$As ($I = 3/2$) spins in silicon using low-field ($< 10$~mT) continuous-wave electrically detected magnetic resonance (EDMR). As the CT condition is approached, pronounced linewidth broadening is observed, consistent with a donor Hamiltonian informed linewidth model. These results establish low-field EDMR as a sensitive probe of CTs in near-surface donor systems relevant to silicon-based quantum devices.

Recent experiments demonstrated that the spin state of individual atoms on surfaces can be quantum-coherently controlled through all-electric electron spin resonance. By constructing interacting arrays of atoms this results in an atomic-scale qubit platform. However, the static exchange coupling between qubits, limited lifetime and polarization of the initial state, impose significant limits on high-fidelity quantum control. We address this issue using open quantum systems simulation and quantum optimal control theory. We demonstrate the conditions under which high-fidelity operations ($\mathcal{F} \gtrsim 0.9$) are feasible in this qubit platform, and show how the Krotov method of quantum optimal control theory adapts to specific noise sources to outperform the conventional Rabi drivings. Finally, we re-examine the experimental setup used in the initial demonstration of this qubit platform and propose optimized experimental designs to maximize gate fidelity in this platform.

That author's affiliation: Rutgers University Institution (first & last author): Rutgers University

We show that a three-dimensional superconductor with a non-Abelian SU(2) order parameter can support an extended resistive regime a Bose metal, in which transport is carried by bosonic electron-Majorana bound states - separating a uniform superconductor from a pair-density-wave (PDW) phase. The setting is a solvable Kondo lattice model introduced previously by the present authors, in which Kondo screening of a Yao-Lee $\mathbb{Z}_2$ spin liquid generates an order parameter with SU(2), rather than conventional U(1), symmetry, containing both superconducting and spin-density-wave components. Two effects cooperate to make fluctuations anomalously strong in three dimensions: the vanishing of the quadratic superconducting stiffness near the Lifshitz point where the optimal pairing momentum shifts from zero to finite $Q$, and the enlarged SU(2) order-parameter manifold. Building on our prior result that doping away from half-filling drives amplitude-modulated PDW order via finite-momentum electron-Majorana condensation, we analyze the fluctuation-dominated regime above that phase using a nonlinear sigma model. We find that the order-parameter propagator develops a ring of soft modes throughout the disordered phase, and that the resulting resistivity scales approximately as $R \sim T^3$ in three dimensions.

That author's affiliation: Martin Luther University, Halle-Wittenberg First author institution: Forschungszentrum Jülich Last author institution: Martin Luther University, Halle-Wittenberg

Chiral spin textures such as skyrmions have attracted considerable attention due to their nontrivial topology, chirality, stability at the nanoscale, and potential for low-power spintronic devices. The recent discovery of intrinsic magnetism in van der Waals (vdW) materials and the ability to engineer their heterostructures has opened a new platform to study and manipulate such textures. In these layered systems, atomically sharp interfaces, strong spin-orbit coupling, and tunable symmetry breaking provide unique opportunities to stabilize and control chiral magnetic states. This review summarizes the fundamental mechanisms underlying the formation of chiral spin textures in vdW heterostructures, including the roles of exchange interactions, magnetic anisotropy, Dzyaloshinskii-Moriya interaction, and dipolar effects. We highlight key experimental advances in the observation and manipulation of chiral textures, discuss their dynamical properties and transport signatures, while overviewing selected theoretical investigations. Finally, we outline current challenges and future directions toward realizing robust, room-temperature chiral spin textures for practical spintronic technologies.

That author's affiliation: TU Delft First author institution: École Polytechnique de Montréal Last author institution: TU Delft

Germanium (Ge) quantum wells are emerging as versatile platforms for quantum devices, supporting high-quality spin qubits and integration with superconducting leads. These applications benefit from strong intrinsic spin-orbit interaction (SOI), enabling efficient electrical control and engineering of spin degrees of freedom. The most advanced Ge/SiGe heterostructures to date, based on compressively strained Ge channels within strain-relaxed silicon-germanium (SiGe) barriers, exhibit weak SOI due to the heavy-hole character of the wave function, posing challenges for spin-based quantum devices and requiring complex device designs for fast qubit manipulation. In this work, we demonstrate that concrete heterostructure modifications can overcome these limitations, enhancing SOI by up to three orders of magnitude. Specifically, we propose to enrich unstrained Ge channels by localized, strained silicon spikes. Leveraging a multi-objective Bayesian optimization, we optimize the spike profile to maximize SOI, while ensuring compatibility with current epitaxial growth processes and robustness against realistic variations of growth parameters. Our heterostructure substantially enhances device performance, yielding up to two orders of magnitude higher quantum-dot spin qubit quality factors than state-of-the-art materials. We also predict GHz-scale spin splittings for hybrid superconducting Andreev spin qubits. These novel Ge heterostructures with engineered Si concentration profiles can open pathways to scalable quantum and spintronic applications.

That author's affiliation: University of Iowa Institution (first & last author): University of Iowa

Solid-state spin defects hold great promise as building blocks for various quantum technologies. Embedding spin centers in $p$-$n$ diodes under reverse bias has proved to be a powerful strategy to narrow the optical linewidth and increase spin coherence, while also enabling control of the photoluminescence wavelength via Stark shift. Given the multitude of parameters influencing spin centers in diodes (e.g., doping densities and profiles, temperature, bias voltage, spin center position), a question that has not yet been answered is: which set of these design parameters maximizes spin center coherence? In this work, we address this question by developing a scaled gradient descent optimization algorithm that minimizes the optical linewidth of spin centers by combining the numerical solution of a diode's Poisson equation with calculated charge noise from the non-depleted regions. Our optimization is performed for both single- and multiple-parameter cases for divacancies in SiC $p$-$i$-$n$ diodes, including reverse-bias voltage, doping density and profile, and diode total length. Importantly, the optimization is subject to realistic physical constraints, such as small operating bias voltages, avoidance of the dielectric breakdown regime and physical thresholds for doping density. Additionally, due to the leakage current at reverse bias voltages, we develop a new formalism to investigate its influence on coherence. We show that the corresponding noise can be mitigated by implanting spin defects away from the diode's surfaces. Our work provides guidance on experimentally relevant diodes for hosting spin centers with the narrowest optical linewidths and longest coherence times.

That author's affiliation: University of Maryland Institution (first & last author): University of Maryland

One of the most important physical effects in condensed matter physics is the Rashba spin-orbit coupling (RSOC), introduced in seminal works by Emmanuel Rashba. In this article, we discuss, describe, and review (providing critical perspectives on) the crucial role of RSOC in the currently active research area of topological quantum computation. Most, if not all, of the current experimental topological quantum computing platforms use the idea of Majorana zero modes as the qubit ingredient because of their non-Abelian anyonic property of having an intrinsic quantum degeneracy, which enables nonlocal encoding protected by a topological energy gap. It turns out that RSOC is a crucial ingredient in producing a low-dimensional topological superconductor in the laboratory, and such topological superconductors naturally have isolated localized midgap Majorana zero modes. In addition, increasing the RSOC strength enhances the topological gap, thus enhancing the topological immunity of the qubits to decoherence. Thus, Rashba's classic work on SOC may lead not only to the realization of localized non-Abelian anyons, but also fault tolerant quantum computation.

That author's affiliation: Nanyang Technological University Institution (first & last author): Nanyang Technological University

Superconducting resonators coupled to solid-state qubits offer a scalable architecture for long-range entangling operations and fast, high-fidelity readout. Realizing this requires low photon-loss rates and qubits with tunable electric dipole moments that couple strongly to the resonator's electric field while maintaining long coherence times. For spin qubits, spin-photon coupling is typically achieved via spin-charge hybridization. However, this introduces a fundamental trade-off: a large spin-charge admixture enhances the coupling strength, which boosts readout and resonator-mediated gate speeds, but exposes the qubit to increased decoherence, thereby increasing the threshold required for strong coupling and limiting the time available for accurate state measurement. This makes it essential to identify optimal operating points for each qubit platform. We address this for the donor-based flip-flop qubit, whose microwave-controllable electron-nuclear spin states make it suitable for coupling to microwave resonators. We demonstrate that, by choosing intermediate tunnel couplings that balance strong interaction with long qubit lifetimes, high-fidelity readout and strong coupling are simultaneously achievable. We also map out the respective charge-photon couplings and photon-loss rates required. Furthermore, we show that experimental constraints on charge-photon coupling and photon loss can be mitigated using squeezed input fields. As similar trade-offs appear in quantum-dot-based qubits, our methods and insights extend naturally to these platforms, offering a potential route toward scalable architectures.

That author's affiliation: Yale University First author institution: Universidad Complutense de Madrid Last author institution: Yale University

Dissipative tunneling remains a cornerstone effect in quantum mechanics. In chemistry, it plays a crucial role in governing the rates of chemical reactions, often modeled as the motion along the reaction coordinate from one potential well to another. The relative positions of energy levels in these wells strongly influence the reaction dynamics. Chemical research will benefit from a fully adjustable, asymmetric double-well equipped with precise measurement capabilities of the tunneling rates. In this paper, we show a quantum simulator system that consists of a continuously driven Kerr parametric oscillator with a third order non-linearity that can be operated in the quantum regime to create a fully tunable asymmetric double-well. Our experiment leverages a low-noise, all-microwave control system with a high-efficiency readout, based on a tunnel Josephson junction circuit, of the which-well information. We explore the reaction rates across the landscape of tunneling resonances in parameter space. We uncover two new and counter-intuitive effects: (i) a weak asymmetry can significantly decrease the activation rates, even though the well in which the system is initialized is made shallower, and (ii) the width of the tunneling resonances alternates between narrow and broad lines as a function of the well depth and asymmetry. We predict by numerical simulations that both effects will also manifest themselves in ordinary chemical double-well systems in the quantum regime. Our work is a first step for the development of analog molecule simulators of proton transfer reactions based on quantum parametric processes.

That author's affiliation: IQM Quantum Computers First author institution: IQM (Germany) Last author institution: University of Würzburg

Near-term fermionic simulation with subspace noise tailored quantum error mitigation

The superconducting diode effect (SDE) enables nonreciprocal supercurrent flow, holding immense potential for ultra-low-power quantum electronics. Intrinsic SDE typically requires materials with inherent symmetry breakings. Here, we report the discovery of SDE in chemical vapor deposition-grown molybdenum carbide ($\mathrm{Mo}_2\mathrm{C}$) nanoflakes, a material traditionally considered centrosymmetric. Strikingly, this system uniquely hosts both field-odd and field-free SDEs. Transport measurements reveal a field-odd SDE with tunable efficiency exceeding 40% at 4 K under a perpendicular in-plane magnetic field. In a separate sample, a robust field-free SDE persists under zero-field and field-coolings. Out-of-plane field sweeps confirm the intrinsic nature of these phenomena. We propose that domain-boundary supercurrents or charge density wave-like orders drive this unexpected combination of symmetry breakings. Our findings establish air-stable $\mathrm{Mo}_2\mathrm{C}$ as an ideal platform for nonreciprocal superconducting electronics operating at liquid-helium temperatures, expanding the search for SDE into nominally centrosymmetric superconductors.

That author's affiliation: Forschungszentrum Jülich Institution (first & last author): Forschungszentrum Jülich

Hybrid superconductor-topological insulator (TI) nanostructures constitute a promising materials platform for exploring proximity-induced superconductivity in systems with topologically protected surface states. A key obstacle has been the realization of clean and well-controlled superconductor-TI interfaces, as TI surfaces rapidly degrade under ambient conditions. Here, we introduce a fully in situ, multi-angle stencil lithography technique that enables the fabrication of proximitized charge islands in TIs. The approach combines selective-area growth of (Bi,Sb)$_2$Te$_3$ nanoribbons with angle-controlled deposition of diffusion barriers, superconducting Al, and ultrathin oxide tunnel barriers, allowing scalable fabrication of hybrid nanostructures without post-growth processing. Low-temperature transport measurements reveal robust Coulomb blockade and a pronounced suppression of low-energy conductance which vanishes with magnetic field, consistent with proximity-induced superconductivity in the island. These results establish a versatile nanofabrication platform that enables access to previously unexplored TI-based hybrid quantum devices and opens new routes for investigating superconductivity in topological nanostructures.

The three-dimensional Hofstadter model exhibits a critical rational flux at which Weyl points emerge in the single-particle spectrum. We study the superconducting regime of the model in the presence of a Hubbard attractive interaction by tuning the magnetic flux across its critical value. We determine the phase diagram in the plane of the coprime pairs parametrizing the magnetic flux. We show that the system exhibits two distinct regimes separated by a critical flux $\Phi_c$: for $\Phi>\Phi_c$, a semimetal-to-superconductor quantum phase transition occurs at a finite interaction strength ($U_c\neq0$), while for $\Phi<\Phi_c$ superconductivity arises for arbitrarily weak attraction, with a BCS-like exponential scaling of the gap due to the finiteness of the density of states. Close to the transition, we study the scaling behavior and identify the critical exponents. Our results highlight the interplay between magnetic band topology and attractive pairing in three-dimensional Hofstadter systems.

The Josephson diode effect (JDE) has attracted significant attention for enabling directional, dissipationless supercurrents, positioning Josephson junctions as promising building blocks for next-generation quantum devices. Hybrid semiconductor-superconductor nanowires provide an experimentally accessible platform for realizing the JDE and hosting Majorana bound states. However, most theoretical treatments assume the single-channel limit, whereas realistic nanowire devices are inherently multichannel due to transverse confinement. Here, we investigate the JDE in multichannel Rashba nanowire Josephson junctions, focusing on the role of inter-subband coupling. We show that subband hybridization qualitatively modifies both the topological phase diagram and the JDE response of the device. In contrast to the single-channel case, the topological phase is confined to a finite window of Zeeman fields, within which Majorana bound states strongly enhance the diode efficiency. Inter-subband coupling also enables a finite JDE even when the Zeeman field is aligned along the spin-orbit direction -- a mechanism absent in independent-channel and strictly one-dimensional nanowire systems. Furthermore, inter-subband coupling enhances spectral asymmetry and significantly increases the diode efficiency compared to single-channel junctions. These results identify inter-subband hybridization as a key ingredient for realizing and optimizing nonreciprocal superconducting transport in experimentally relevant hybrid nanowire Josephson junctions.

We theoretically demonstrate a practical method for tuning randomly disordered 2D quantum-dot grids underlying spin qubit platforms using vision-based neural networks trained on tensor-network generated charge-stability data. We show that a simulatable local $3\times 3$ window already contains sufficient information to tune the central dot within a much larger array, thereby validating a sliding-window approach in which one tunes a local region and then translates that window across the lattice to calibrate a larger device. This avoids the computationally intractable necessity for obtaining the ground states for large systems with exponentially large Hilbert space. For the experimentally relevant case where only the on-site disorder is unknown, the neural network predicts the relevant parameters with very high fidelity in the $3\times 3$ setting [$R^2 >0.99$], and after fine tuning on only a small number of larger-device samples, it retains high accuracy for the central dot of a $5\times 5$ plaquette [$R^2\approx 0.98$]. When all the dots parameters are treated as unknown, prediction of the on-site disorder remains robust [$R^2>0.9$ for both $3\times 3$ and $5\times 5$], although the remaining parameters are substantially more difficult to infer from the same charge-stability data. This shows that the most practically important disorder parameter for tuning can still be inferred reliably even in the fully disordered setting for the computationally difficult 5x5 arrays.

Magnetic domain walls have long been pursued as carriers of classical information for storage and processing. With the ability to create, control, and probe domain walls at the nanoscale, they are recently recognized as an ideal platform for studying macroscopic quantum effects and provide a natural blueprint for building scalable quantum computing architectures. In particular, the experimentally demonstrated high mobility of domain walls makes them not only suitable as stationary qubits but also as flying qubits, which may offer advantages over currently explored quantum computing platforms. In this Perspective, we outline our current understanding of the essential ingredients and key requirements for realizing universal quantum computation based on magnetic domain walls. We highlight promising concrete material platforms and identify the experiments that are still needed to advance this concept. We also discuss the potential challenges and point to new opportunities in this emerging research direction at the interface between magnetism and quantum information science.

Recent experiments on a range of engineered quantum systems have highlighted the important role of interacting two-level systems (TLSs) in modifying device properties and generating fluctuations. Focusing on the case of an oscillator coupled to a single near-resonant TLS, we explore how interactions between the TLS and lower-frequency thermally activated two-level fluctuators (TLFs) degrade the oscillator's coherence. Depending on the strength of the couplings, a single TLF can give rise to coherence oscillations that appear alongside, or supplant, Rabi oscillations of the oscillator-TLS system. Bath-driven transitions in the TLF cause irreversible coherence decay at a rate that is highly sensitive to both the couplings and the transition rate. For an ensemble of TLFs, we identify and characterise the different regimes of non-exponential phase-averaging-driven coherence decay that the oscillator can display. Using numerical calculations, we examine the extent to which systems with just a few TLFs differ from the limit of a large (continuum) TLF ensemble. Our work provides a theoretical framework for understanding the interplay of coherent TLS interactions and TLF-induced dephasing in quantum devices such as superconducting and phononic resonators.

Majorana zero modes (MZMs) are bound midgap topological excitations at the ends of a 1D topological superconductor, which must come in pairs. If the two MZMs in the pair are sufficiently well-separated by a distance much larger than their individual localization lengths, then the MZMs behave as non-Abelian anyons which can be braided to carry out fault-tolerant topological quantum computation. In this `topological' regime of well-separated MZMs, their overlap is exponentially small, leading to exponentially small Majorana splitting, thus enabling the MZMs to be topologically protected by the superconducting gap. In real experimental samples, however, the existence of disorder and the finite length of the 1D wire considerably complicate the situation, leading to ambiguities in defining `topology' since the Majorana splitting between the two end modes may not necessarily be small in disordered wires of short length. We theoretically study this situation by calculating the splitting in experimentally relevant short disordered wires, and explicitly investigating the applicability of the `exponential protection' constraint as a function of disorder, wire length, and other system parameters in realistic models of nanowires currently being used experimentally. We find that the exponential regime is highly constrained, and is suppressed for disorder somewhat less than the topological superconducting gap. We provide detailed results and discuss the implications of our theory for the currently active experimental search for MZMs in superconductor-semiconductor hybrid platforms. A general consequence of our work is that `topology' in finite disordered wires may not be uniquely defined, necessitating a careful analysis which depends on the context.

Distributed quantum inner product estimation with structured random circuits

Two-qubit gates using on-demand single-photons from ordered shape and size controlled large-volume superradiant quantum dots

The ultrastrong coupling regime of cavity photons and quantum materials has emerged as a pathway to modify materials properties, however definitive signatures of ultrastrong coupling remain elusive. Focusing on the quantum photon statistics of light transmitted through a cavity-embedded superconductor, we show that a two-photon Higgs polariton at strong coupling realizes a photonic nonlinearity at the single terahertz photon level. We find that as light-matter coupling increases, the photon statistics show pronounced changes due to the formation of a hybrid photon-matter dark-cavity state with finite photon occupancy, producing testable signatures of ultrastrong coupling. We derive a non-Markovian input output relation and study the cavity-embedded superconductor 2H-NbSe2 as it approaches ultrastrong light-matter coupling. Our results reveal a diagnostic for ultrastrong coupling in the two-photon coincidence statistics that is absent in total counts.

Flux-tunable superconducting qubits rely on fast flux control pulses to implement two-qubit entangling quantum gates, a key building block for quantum algorithms. However, distortion effects introduced by non-ideal control electronics, parasitic components, and the cryogenic quantum chip response can all degrade the gate fidelity. We present a digital predistortion (DPD) framework for characterizing and then compensating for these distortions using a combination of infinite impulse response (IIR) and finite impulse response (FIR) filters. Experiments on a flux-tunable quantum processing unit (QPU) demonstrate a successful correction of step-response distortions on the flux-control line, with a compensated control signal showing only sub-percent deviations from the ideal target linear behavior. The demonstrated method enables automated rapid calibration of flux control channels for superconducting QPUs.

That author's affiliation: Universidad de Zaragoza Institution (first & last author): Universidad de Zaragoza

Laser nitriding represents a versatile approach for tailoring the surface properties of metals. Up to now, its effect on the superconducting response of niobium nitrides remains largely unexplored. In this work, the nitriding process of niobium by laser irradiation under a controlled nitrogen atmosphere up to 2.50 bar, using a nanosecond pulsed laser with wavelength of 1064 nm has been investigated. By independently tuning the nitrogen pressure, the two-dimensional accumulated fluence ($F_{2D}$) and the laser irradiance, a laser-processing map for the formation of either a combination of $\beta$-Nb$_2$N (hexagonal) and $\gamma$-Nb$_4$N$_{3\pm x}$ (tetragonal) phases or only the $\beta$-phase has been established. Systematic analysis by X-ray diffraction, scanning electron microscopy and electron backscatter diffraction revealed that the nitrogen-rich $\gamma$-phase forms in the near-surface layer through melting when $F_{2D}$ exceeds a certain value ($> 50 \,\mathrm{kJ/cm^2}$ at 2.50 bar). A $\beta$-layer is observed underneath, and further inside, there is a band of embedded $\beta$-grains in the Nb matrix. Their size gradually decreases with increasing distance to surface, suggesting thermal gradients and a diffusion formation mechanism. When the $\gamma$-phase becomes predominant, a significant increase in the superconducting critical temperature is observed, up to $T_c \approx 15\,\mathrm{K}$, and magnetic irreversibility. For low $F_{2D}$ values ($\approx 7.5 \,\mathrm{kJ/cm^2}$ at 1.50-2.50 bar), the formation of a uniform nitride layer composed of sub-micron-sized $\beta$-Nb$_2$N grains results in a ca. fourfold enhancement in surface microhardness. These findings provide fundamental insights into laser-induced nitriding of niobium to engineer mechanically robust and superconducting Nb-N layers.

Quantum technologies promise a radically new way to solve classically intractable computing problems. Superconducting circuits as a platform are at the forefront of this field. The cryogenic operation temperatures of superconducting circuits however impose challenges for the further scaling to many connected quantum information processing units into a local area or global network. In this work, we present a hardware solution for connecting quantum devices operating at microwave frequencies into local area networks, which enable the exchange of quantum information between spatially separated parties. Specifically, we demonstrate a modular system spanning distances of 5, 10 and 30 meters operated at cryogenic temperatures and connecting two superconducting circuit systems, located in individual dilution refrigerators, through a quantum communication channel. We develop a thermal model to evaluate the heat transfer processes in the setup, optimize the design and select appropriate materials for its construction. The assembled 30-meter-long system achieves operating temperatures of below 50 mK after a cooldown time of about six and a half days. This link enables the execution of distributed quantum computing and communication algorithms. It also adds the resource of non-locality, certified by a loophole-free Bell test, to the field of quantum science and technology with superconducting circuits.

Mechanical resonators operating in the megahertz range have become a versatile platform for fundamental and applied quantum research. Their exceptional properties, such as low mass and high quality factor, make them also appealing for force sensing experiments. In this work, we propose a method for detecting, and ultimately controlling, nuclear spins by coupling them to megahertz resonators via a magnetic field gradient. Dynamical backaction between the sensor and an ensemble of $N$ nuclear spins produces a shift in the sensor's resonance frequency. The mean frequency shift due to the Boltzmann polarization is challenging to measure in nanoscale sample volumes. Here, we show that the fluctuating polarization of the spin ensemble results in a measurable increase of the resonator's frequency variance. On the basis of analytical as well as numerical results, we predict that the variance measurement will allow single nuclear spin detection with existing resonator devices.

This study maps the quantum landscape of superconducting diodes (SDs) \cite{nadeem23} onto the quantum technology architecture, which is currently constrained by fundamental challenges in control and scalability. In the existing non-integrated quantum technology hardware, control and scalability related issues emerge at two fronts: First, nonlinear and nonreciprocal circuit elements, which are essential building blocks for quantum processors, are often complex, bulky, and dissipative. Second, the temperature gradient between classical control electronics ($T_C\gtrsim$ K), which is also dissipative, and the quantum processor at cryogenic temperatures ($T_Q\sim$ mK) makes scalability even more challenging. The main focus is to reveal how the built-in nonlinearity, nonreciprocity, and quantum functionalities of SDs are significant for on-chip integrated circuit quantum electrodynamics (c-QED), enabling scalable integration of noise-resilient qubit and qubit-interfaces for efficient power delivery, coherent control and memory, high-fidelity readout, and quantum-limited amplification. To this end, this study will also shed light on how thermodynamic constraints and field effects can be harnessed within a quantum-enhanced SD platform, thereby enabling thermal compatibility between classical and quantum workflows, isothermal all-electrical control, and on-chip scalability. This perspective is expected to play a pivotal role in the advancement of superconducting circuit-based quantum hardware with temperature-matched classical, quantum, and hybrid workflows.

We present a theory of ballistic N/F/S and S/F/S junctions with a uniformly precessing magnetization, which generates long-range equal-spin superconducting correlations [Takahashi et al., Phys. Rev. Lett. 99, 057003 (2007), Houzet, Phys. Rev. Lett. 101, 057009 (2008)]. The non-equilibrium distribution of Andreev bound states leads to a strongly non-sinusoidal current-phase relationship for large precession angles. We derive detailed results for ballistic junctions involving partially and fully polarized ferromagnets. In the fully polarized half-metal limit, the magnetization precession switches the junction from an "off" state with vanishing subgap current to an "on" state with finite Andreev conductance and finite Josephson current.

We theoretically study the direct and inverse spin Hall effects in a superconductor-normal metal-superconductor junction induced by a spin-orbit interaction that is invariant under spatial inversion. We show that a supercurrent induces a spin Hall effect, leading to a static spin accumulation with opposite polarizations at the two edges, analogous to that in normal conductors. For the inverse effect, we consider a spatially inhomogeneous static magnetic field and show that it induces an anomalous phase shift, which, in the presence of higher harmonics, results in a diode effect. Unlike Rashba systems, the present mechanism does not require broken structural inversion symmetry.

Over the last decade, the development of Josephson devices based on van der Waals (vdW) materials has advanced rapidly, representing a paradigm shift driven by the advent of 2D materials. The diverse vdW materials library, combined with advanced fabrication techniques, enables the integration of materials with vastly disparate properties for scientific exploration. The vdW Josephson junctions (JJs) offer a unique route to explore novel functionalities and associated physics that remain inaccessible in conventional JJs, which have reached an industrial level in terms of fabrication. Beyond material diversity, vdW crystalline materials offer fundamental new control over device symmetries, enabling the realization of Hamiltonians unique to 2D systems. Furthermore, the long relaxation times of myriad excitations in 2D heterostructures open possibilities for creating exquisite quantum sensors, with the 2D material itself acting as an efficient bus for transmitting excitations to the active sensing element. This creative explosion in vdW-based superconducting electronics is rapidly growing, and our review highlights the resulting devices and physics. The confluence of vdW JJs with twistronics and topology has the potential to redefine superconducting quantum technology, enabling applications from quantum computation to ultra-sensitive hybrid sensors. While opportunities abound with vdW JJs, the challenge of scalability must be surmounted for translation into real-world devices. This review synthesizes current developments and offers a roadmap for researchers navigating this burgeoning field.

We explore the expected performance of a semiconducting spin cQED quantum processor for Multiple Hypothesis Tracking (MHT) algorithm via a quantum annealing procedure. From two different benchmarking scenarios we evaluate this type of quantum annealer on a quantum emulator in which we incorporated both dynamical coherent errors and incoherent errors. From estimate of the reset, measurement and annealing time of the processor, we find that cQED-spin processors could reach a total run time of around 50 ms. This makes this technology promising for potential real time application such as radar tracking.

The supercurrent diode effect (SDE), characterized by unequal critical currents in opposite directions, has been observed with or without magnetic fields, yet mechanisms enabling zero-field SDE without explicit symmetry breaking remain underexplored. Here we investigate a Josephson junction with strong electron-electron interaction modeled by a Hubbard $U$ term and an odd number of electrons. We find that strong correlations induce spontaneous breaking of time-reversal and mirror symmetries, forming a $\varphi$-junction with degenerate energy minima at $\pm\varphi$, resulting in zero-field Josephson diode effect (JDE) without magnetic order. Spin-orbit coupling breaks SU(2) symmetry but does not determine diode polarity, contrasting with magneto-chiral mechanisms. We further show that applying a tiny Zeeman field enables controllable JDE with sizable efficiency due to the enhancement by the strong magnetic correlation, and the JDE strength peaks when the field induces a level-crossing transition. These findings establish strong electron correlation as a distinct mechanism for nonreciprocal superconducting transport, broadening the understanding of SDE origins.

Tuning of gate-defined semiconductor quantum dots (QDs) is a major bottleneck for scaling spin qubit technologies. We present a deep learning (DL) driven, semantic-segmentation pipeline that performs charge auto-tuning by locating transition lines in full charge stability diagrams (CSDs) and returns gate voltage targets for the single charge regime. We assemble and manually annotate a large, heterogeneous dataset of 1015 experimental CSDs measured from silicon QD devices, spanning nine design geometries, multiple wafers, and fabrication runs. A U-Net style convolutional neural network (CNN) with a MobileNetV2 encoder is trained and validated through five-fold group cross validation. Our model achieves an overall offline tuning success of 80.0% in locating the single-charge regime, with peak performance exceeding 88% for some designs. We analyze dominant failure modes and propose targeted mitigations. Finally, wide-range diagram segmentation also naturally enables scalable physic-based feature extraction that can feed back to fabrication and design workflows and outline a roadmap for real-time integration in a cryogenic wafer prober. Overall, our results show that neural network (NN) based wide-diagram segmentation is a practical step toward automated, high-throughput charge tuning for silicon QD qubits.

Spin shuttling has crystalized as a powerful and promising tool for establishing intermediate-range connectivity in semiconductor spin-qubit devices. Although experimental demonstrations have performed exceptionally well on different materials platforms, the question of how to handle areas of low valley splitting in silicon during shuttling remains unresolved. In this work, we explore the possibility of utilizing the valley degree of freedom, particularly in regions of low valley splitting, to allow mobile spin qubits to be shuttled through an occupied stationary quantum dot, thereby leapfrogging over the stationary electron. This not only grants a more enriched mobility for shuttled electrons, as it opens new possible routing paths, but also enables the implementation of an entangling SWAP$^\gamma$ two-qubit gate operation in the process. Simulating this process for different sets of parameters, we demonstrate the feasibility of such an operation and offer a unique use case for otherwise precarious regions of a quantum processor chip and propose a possible extension to the set of possible operations for silicon spin qubit devices.

Spin qubits have emerged as a leading platform for quantum information processing due to their long coherence times, small footprint, and compatibility with the existing semiconductor industry. We first provide an introduction to the different qubit implementations currently being investigated, including single electron-spin qubits, hole-spin qubits, donor qubits, and multispin encodings. We discuss how the confinement and strain present in semiconductor heterostructures produce addressable levels whose spin degree of freedom can be used to encode a qubit. A large emphasis is placed on reviewing the theoretical foundations and recent experimental demonstrations of proposed mechanisms for long-range coupling, including hybrid approaches based on circuit QED and Andreev qubits, as well as spin shuttling. Finally, we review a recent proposal for linking spin qubits using topological spin textures.

We study $\mathbb{Z}_3$-symmetric Rabi model that describes a three-level system coupled to two bosonic modes. We derive a mapping of the two-mode $\mathbb{Z}_3$ Rabi model onto a qubit-boson ring. This mapping allows us to formulate a realistic implementation of the $\mathbb{Z}_3$ Rabi model based on superconducting qubits. It also provides context for the previously proposed optomechanical implementation of the $\mathbb{Z}_3$ Rabi model. In addition, we propose a physical implementation of the $\mathbb{Z}_3$ Potts model via a coupled chain of $\mathbb{Z}_3$ Rabi models.

Superconducting diodes enable dissipationless directional transport, yet achieving electrical tunability and scalability remains a major challenge for circuit-level integration. Here, we demonstrate an electrothermal-switch superconducting diode in which a gate-controlled nanoscale hotspot dynamically breaks inversion symmetry in a superconducting nanowire. This mechanism gives rise to two coexisting nonreciprocal transport regimes-one associated with a nonreciprocal superconducting-to-normal transition and the other with ratchet-like vortex dynamics-both originating from the same electrothermal-switch process. The diode exhibits efficiencies up to 42% and 60% for the two regimes, respectively, and can be electrically switched on, off, or reversed in polarity in situ by applying a small gate current. These capabilities enable programmable superconducting circuits that realize electrically reconfigurable full-wave and half-wave rectification. The lithography-compatible design, high performance, and gate-controlled functionality establish a scalable platform for programmable superconducting electronics and hybrid quantum systems.

We investigate the Josephson coupling between two superconducting electrodes connected by a ferromagnetic racetrack hosting a Bloch-like domain wall (DW). We show that the interplay between superconductivity and the DW leads to highly non-trivial spatial distributions of the supercurrent, including the formation of current loops and a strong sensitivity to the DW position and orientation. We further demonstrate that the Josephson critical current $I_c$ can be efficiently controlled by the DW position along the racetrack, exhibiting pronounced variations and tunable $0$--$\pi$ transitions. These results provide clear design principles for superconducting racetrack devices and establish domain walls as a viable control element for readout schemes in racetrack memory architectures.

We investigate electron paring in two-dimensional electron systems mediated by the vacuum fluctuations of a quantized magnetic flux generated by the inductor of an LC resonator. The interaction induces long-range attractive interactions between angular momentum states which lead to pairing in a broad class of materials with critical temperatures of few Kelvin or even higher, depending on the field-covered area. The induced state is a pair-density wave topological chiral superconductor. The proposed platform in circuit QED environment offers a tunable promising tool for engineering electron interactions in two-dimensional systems to create new quantum phases of matter.

In a hybrid system where two quantum dots (QDs) are coupled to a conventional $s$-wave superconductor, Poor Man's Majorana modes (PMMs) have been proposed. Existing theories often idealize the superconductor (SC) as a bulk system or an infinitely long chain, or treat it as another quantum dot with proximity-induced superconductivity, while experiments employ superconducting segments of finite length. Here, we model the SC as a finite-length 1D chain and treat the QDs and SC on equal footing. We obtain the conditions for the existence of PMMs, valid for arbitrary SC length and applicable to arbitrary tunneling strengths and magnetic fields. We find that the number of PMMs is highly sensitive to the SC length: it oscillates between zero and two with a period set by the Fermi wavelength ($\sim1\,\text{\AA}$), while four PMMs appear in the long-SC limit where the effective coupling between the two QDs becomes negligible. We further demonstrate that the PMMs that are separately localized at the two ends of the hybrid system do not exist in the finite-length case. Consequently, only nearly localized PMMs can be identified when the magnetic field is strong enough. In this way, the generalized `sweet spot' of the practical system can be found.

Decoherence and dissipation, arising from unavoidable interactions with the environment, can exert a dual influence on transport in physical systems, suppressing coherent propagation while inducing diffusion and mitigating localization in disordered systems. Non-Hermitian physics reveals a qualitatively different scenario, in which structured dissipation can induce directional bulk-to-boundary transport, known as the non-Hermitian skin effect (NHSE), that remains robust against disorder. Whether such transport can persist, be enhanced or hindered under decoherence, remains a largely open question. Here we experimentally address this question using photonic quantum walks with two tunable prototypical decoherence channels, dephasing and amplitude damping. Under dephasing, the NHSE survives up to the fully incoherent regime and is observed to even be enhanced by dephasing, yielding drift velocities that exceed those of coherent dynamics. By contrast, amplitude damping shows a pronounced order dependence: applied before the non-Hermitian loss operator, it suppresses and ultimately eliminates the NHSE in the fully incoherent limit; applied afterward, the NHSE persists and can be enhanced at sufficiently large loss strengths. Our work bridges quantum and classical non-Hermitian dynamics, demonstrates the resilience of the NHSE to decoherence, and opens avenues for harnessing decoherence to enhance directional transport in noisy, nonequilibrium systems.

We investigate Coulomb drag in a system of two capacitively coupled superconducting nanowires. In this context, drag refers to the appearance of a stationary voltage in the passive wire in response to a current bias applied to the active one. Quantum phase slips (QPS) in the biased wire generate voltage fluctuations that can be transmitted to the other. Using perturbative and semiclassical approaches, we show that when both wires are superconducting the induced voltage vanishes due to exact cancellation of plasmon contributions. By contrast, when the second wire is tuned below the superconductor-insulator transition and develops a mass gap, this cancellation is lifted and a finite drag voltage emerges. The drag coefficient exhibits a crossover from weak drag in short wires to a maximal value set by the mutual capacitance in long wires. A semiclassical picture of voltage pulse propagation clarifies the physical origin of the effect: the mass term synchronizes plasmon modes and prevents complete cancellation of induced signals. Our results establish a mechanism of mass-induced Coulomb drag in low-dimensional superconductors and suggest new routes for probing nonlocal transport near quantum criticality.

We predict a supercurrent-driven N\'eel spin-orbit torque in a superconductor/$d$-wave altermagnet heterostructure, associated with the emergence of spin-triplet correlations. The effect can be understood as a consequence of the supercurrent-induced spin polarization, owing to the interplay between spin-orbit coupling and momentum-dependent spin splitting, as found, for example, in altermagnets. Remarkably, the supercurrent can be tuned by the N\'eel-vector direction, and the supercurrent-induced torque can both propel magnetic domain walls and reverse the N\'eel-vector orientation within a domain wall. These findings establish superconductor/altermagnet heterostructures as a versatile platform for the dissipationless control of the N\'eel vector, with potential applications in racetrack memory, dissipationless superconducting electronics, and unconventional computing.

We investigate the decay dynamics of a three-level artificial atom, a superconducting transmon qubit, weakly coupled to a continuum of modes in a broadband, one-dimensional cavity. Using the resolvent formalism, we derive analytical expressions for the resonance frequency shifts and widths, which are then evaluated numerically for a Gaussian density of states. We identify two distinct dynamical regimes, differentiated by the ratio of the qubit's coupling strength to the continuum bandwidth. When this ratio is much less than one, the system exhibits a Markovian regime in which the resonance width is practically independent of energy within the continuum band. As the ratio increases, the system transitions to a non-Markovian regime where the resonance width becomes strongly energy-dependent. In this regime, the qubit interacts with the continuum faster than the continuum can erase the information from the qubit's past. Furthermore, we demonstrate that the coupling between the transmon's second level and its ground state significantly influences the decay dynamics of the third level. The interaction between these two levels opens a fast two-photon decay channel, which broadens the transmon's second level.

Superconducting Quantum Interference Devices (SQUIDs), formed by incorporating Josephson junctions into loops of superconducting material, are the backbone of many modern quantum sensing systems. It has been demonstrated that, by combining multiple SQUID loops into a two-dimensional (2D) array, it is possible to fabricate ultra-high-performing Radio frequency sensors. However, to function as absolute magnetometers, current-in-use arrays require the area of each SQUID loop in the array to be incommensurate. Doing so forbids the achievement of their full potential of performance, limited only by the standard quantum limit. This is because imposing incommensurability in the areas contrasts with optimised performance in each single SQUID loop. In this work, we report that by selectively inserting bare sections of a superconducting circuit with no Josephson junctions, 2D SQUID arrays can operate as an absolute magnetometer even when no physical area spread is applied. Based on a generalisation of current available theories, a complete analytical formulation for the one-to-one correspondence between the distribution of these bare loops and what we call a synthetic area spread is unveiled. This synthetic spread represents the equivalent physical spread of incommensurate SQUID loops that you would use to obtain the absolute Voltage-Magnetic Flux response if no bare loops were in use. Our work opens the way to a broader use of this technology for the fabrication of ultra-high-performance absolute quantum sensors. Our approach is also experimentally verified by fabricating several 2D Superconducting Quantum Interference Filter (SQIF) arrays incorporating bare superconducting loops and by demonstrating that they behave in alignment with what is suggested by our theory.

We investigate the electronic transport properties of a superconductor-quantum dot-superconductor Josephson junction coupled to a ferromagnetic metal reservoir in the presence of an external magnetic field. The device is described by an effective non-Hermitian Hamiltonian, whose complex eigenvalues encode the energy (real part) and the broadening (imaginary part) of the Andreev quasi-bound states. When extending the Andreev current formula to the non-Hermitian case, a novel contribution arises that is proportional to the phase derivative of the levels broadening. This term becomes particularly relevant in the presence of exceptional points (EPs) in the spectrum, but its experimental detection is not straightforward. We identify optimal Andreev spectrum configurations where this novel current contribution can be clearly highlighted, and we outline an experimental protocol for its detection. We point out that the phase dependence in the levels imaginary part originates from the breaking of a time-reversal-like symmetry. In particular, spectral configurations in the broken phase of the symmetry and without EPs can be obtained, where this novel contribution can be easily resolved. The proposed protocol would allow to probe for the first time a fingerprint of non-Hermiticity in open junctions that is not strictly related to the presence of EPs.

Scalable spin-based quantum computing demands precise and stable control of a large number of gate-defined quantum dots while minimizing wiring complexity and thermal load. Control architectures based on sample-and-hold (SH) multiplexing techniques offer a promising solution by enabling sequential programming of several gate voltages using a limited number of input lines. However, the compatibility of such dynamic voltage refreshing with the stringent stability, noise, and speed requirements of quantum dot operation is an active subject of study. Here we experimentally demonstrate that a multiplexing cryo-CMOS circuit can reliably bias a silicon double quantum dot (DQD) at 0.5K. Exploiting the isolated regime, we show deterministic loading and isolation of four electrons and stable access to all five charge configurations from (4,0) to (0,4), despite the sequential voltage refreshing. We further demonstrate rapid voltage pulsing across an inter-dot transition, resolving single-electron tunneling events and stochastic switching at the (1,3)-(0,4) transition. These results confirm that SH-based multiplexed control is compatible with both static biasing and pulsing of isolated quantum dots, representing an important milestone toward scalable cryogenic control architectures for large-scale spin-qubit processors.

Planar cavity magnonics has been developed predominantly for a single magnetic film, leaving the role of multiple magnetic layers in a cavity-scattering framework with spatial resolution largely unexplored. In this study, we introduce a bilayer planar cavity in which two magnetic films are embedded inside the same microwave cavity and interact through the cavity field and their relative placement within the standing-wave pattern. First, we derive a full two-film scattering theory in the macrospin limit and recover the exact zero-gap half-thickness limit to benchmark it against the known one-film planar result. This formulation reveals that the bilayer does not simply strengthen the magnon-photon interaction by adding magnetic material but instead enables position-dependent control of the collective bright channel. Antinode-compatible placements enhance effective coupling, whereas node-compatible placements suppress it. We then show that weak symmetry breaking between the two films transfers the finite cavity weight to a mode that is dark in the symmetric limit, producing an additional spectroscopic branch without immediately destroying the main avoided crossing. To extend the analysis beyond the macrospin regime, we formulate a reduced multimode bilayer theory for $J\neq 0$, where odd standing-spin-wave families reorganize into family-resolved bright and dark bilayer channels. Our results show that bilayer planar cavities are a minimal but versatile setting for controlling the collective magnon-polariton structure through geometry, symmetry, and exchange-driven mode hierarchy.

We study two spatially separated boundary subsystems coupled to a common structured environment under relative motion in a Gaussian open-system framework. By integrating out the environment, we obtain an influence functional governed by a dressed environmental correlator evaluated at the boundary positions, which encodes both coherent mediation and correlated fluctuations. Relative motion opens a correlated decoherence channel through Doppler-shifted spectral overlap of the boundary excitations, leading to a kinematic threshold at $v>2u_\phi$. Below threshold, the dominant resonant contribution to the off-diagonal noise kernel is absent and the environment acts predominantly as a coherent mediator at leading resonant order. Above threshold, a resonant shell opens and the same environment supports a finite cross-noise channel, producing irreversible correlated decoherence. In the reduced dynamics, coherent coupling is governed by the retarded component of the dressed correlator, while the decoherence rate is controlled by its Hadamard component. These results establish a direct connection between motion-induced excitation production and correlated decoherence in open quantum systems, and point to experimentally accessible signatures in superconducting--phononic platforms through excess correlated dephasing.

The speed and fidelity of dispersive readout of superconducting qubits should improve by increasing the amplitude of the measurement drive. Experiments show, however, that beyond some drive amplitude there is always a saturation or drop in fidelity, often associated with a decrease in qubit energy relaxation time $T_1$. A simple Lindblad master equation does not capture the latter effect. More involved approaches based on effective master equations rely on strong assumptions about the spectra of the system and the bath and only partially agree with observations. Here, we perform a first-principles simulation of the full unitary dynamics of dispersive readout by considering the circuit QED Hamiltonian coupled to a microscopic model for the measurement transmission line, allowing for its arbitrary spectrum, including filters. Our access to the dynamics of the bath degrees of freedom allows us to investigate the emission spectrum of the system as a function of drive power. We show how the dependence of qubit $T_1$ on readout drive amplitude is sensitive to the details of the bath spectrum. In particular, we find that $T_1$ drops with increasing drive amplitude when a Purcell notch filter is placed at the qubit frequency, and that the Lindblad master equation shows general qualitative defects compared to the first-principles model.

Waveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are structured aperiodically according to the deterministic Fibonacci-Lucas substitution rule. These "Fibonacci waveguides" lack translational invariance and are characterized by a singular continuous energy spectrum and critical eigenstates, representing a deterministic intermediate between ordered and disordered systems. We demonstrate how to achieve decoherence-free, coherent interactions in this unique setting. We analyze two paradigmatic cases: (i) Giant emitters resonantly coupled to the simplest aperiodic version of a standard waveguide. For these, we show that atom photon bound states form only for specific coupling configurations dictated by the aperiodic sequence, leading to an effective atomic Hamiltonian, which itself inherits the Fibonacci structure; and (ii) emitters locally and off-resonantly coupled to the aperiodic version of the Su-Schrieffer-Heeger waveguide. In this case the mediating bound states feature aperiodically modulated profiles, resulting in an effective Hamiltonian with multifractal properties. Our work establishes Fibonacci waveguides as a versatile platform, which is experimentally feasible, demonstrating that the deterministic complexity of aperiodic structures can be directly engineered into the interactions between quantum emitters.

Low-energy electronic behavior in graphite crystals is highly dependent on the relative stacking arrangement of the constituent layers. Topologically non-trivial electronic states can arise due to interrupted rhombohedral (ABC) stacking, localized at the edges of the stacking region, but not in the case of Bernal (AB) stacking. Here, we study the electronic properties of junctions between half-crystals of graphite of either Bernal or rhombohedral stacking, using a charge self-consistent tight-binding method and embedding potentials to account for the influence of layers far from the junction. We find junction-localized electronic states to be a ubiquitous feature, and all systems but one involving a rhombohedral half-crystal support a flat-band expected to exhibit electronic instabilities and strongly-correlated states. Nascent flat-band states associated with finite rhombohedral stacking sequences extend the physics into pure Bernal systems.

We investigate the critical current in microwave-irradiated Josephson junctions hosting Yu-Shiba-Rusinov states due to magnetic impurities. Under two conditions, namely, (i) the breaking of particle-hole symmetry in the normal sense by non-zero potential scattering, and (ii) the breaking of inversion symmetry either by unequal magnitudes of potential scattering and/or magnetic moments, microwave irradiation induces an additional phase-independent contribution to the current. This leads to asymmetric critical currents for opposite current polarities, an effect absent in the same junction without microwave irradiation. The asymmetry is highly tunable via the microwave amplitude and frequency, and we may even achieve perfect asymmetry where the critical current vanishes for one polarity, akin to a perfect diode. While Yu-Shiba-Rusinov states provide the ideal platform for a pronounced asymmetry, we find that as long as the two conditions (i) and (ii) above are met, our proposal does not necessarily depend upon them.

Coupling tailored electromagnetic fluctuations to materials provides a resource for controlling correlated quantum matter. By structuring the frequency, spatial, and modal distribution of fluctuations through a new generation of cavity quantum materials, vacuum and thermal spectra can shift phase boundaries and stabilize or suppress orders. This review organizes the field around a fluctuation-focused perspective, surveying a practical design toolbox and recent milestones, and outlining theory-experiment challenges in realistic, multimode, beyond-long-wavelength regimes. We highlight photonic observables and map opportunities for equilibrium and driven control across superconducting, magnetic, moire, and topological platforms.

We study time-domain electron interferometry in a Hong-Ou-Mandel (HOM) geometry, where a thin superconductor between two quantum Hall systems acts as the beam splitter. By comparing the measurable current cross correlations at the interferometer outputs with those of a normal-conducting electronic HOM setup, we show that Andreev processes strongly affect the HOM dip. Using a combination of scattering theory and numerical tight-binding simulations for a graphene quantum Hall bar, we show that the change of charge cross correlations can be used to experimentally detect and characterize local and crossed Andreev processes.

Low-frequency charge noise induced by fluctuating electrostatic disorder is a major limitation for semiconductor hole spin qubits. Here, we analyze the quasistatic response of a hole spin qubit to individual two-level fluctuators (TLFs). We show that, due to the anisotropy of the g-tensor, the qubit response depends on the geometry of the fluctuator-induced dipolar perturbation. We then propose a readout protocol that isolates selected g-tensor components through an accumulated Berry phase and estimate, within our readout model, an order-unity signal-to-noise ratio with a total protocol time in the tens of microseconds. Finally, using microscopic simulations, we compute the quantum Fisher information (QFI) to identify magnetic field directions and confinement regimes in which the qubit is most sensitive to disorder-induced variations of selected g-tensor components.

Achieving sufficiently low residual excited-state populations remains a key challenge in superconducting quantum circuits, particularly for protocols operating close to noise limits or requiring repeated qubit initialization. Existing protocols primarily address this challenge through sophisticated control, engineered dissipation, or feedback mechanisms. Here, we demonstrate an alternative approach in which a superconducting qubit is reset using a physically distinct, intrinsically colder phononic bath. Specifically, we interface a transmon with a high-overtone bulk acoustic resonator (HBAR), enabling cooling of the qubit into GHz-frequency modes. Using this approach, we achieve a residual excited-state population of the qubit below $10^{-4}$, representing an improvement of one to two orders of magnitude compared to existing reset schemes. These results highlight the potential of phononic baths as a resource for high-fidelity qubit initialization in superconducting circuits.

We introduce a driven-dissipative Floquet model in which a single harmonic oscillator, with both frequency and decay rate modulated, realizes a non-Hermitian synthetic lattice with an effective electric-field gradient in frequency space. Using the Floquet-Green's function and the doubled Hamiltonian representation of non-Hermitian matrices, we show that the linear response of this system is characterized by a local winding number. Nontrivial values of the winding number induce directional amplification in the synthetic dimension, thereby converting input signals to different frequencies. The underlying mode structure is well described by a Jackiw-Rebbi-like continuum theory with Dirac cones and solitonic topological zero modes in synthetic frequency. Our results establish a simple and experimentally feasible route to non-Hermitian topological amplification, naturally implementable in current quantum technologies such as superconducting circuits.

In a recent paper [arXiv:2205.06279], Danielson et al. demonstrated that the mere presence of a black hole causes universal decoherence of quantum superpositions (dubbed the DSW decoherence). We analyze decoherence in a superconducting analogue [arXiv:1709.06154] of the event horizon of a black hole, where Andreev reflection plays the role of Hawking radiation. We consider a normal metal interferometer threaded by an Aharonov-Bohm flux, where one of the arms of the interferometer is coupled to a superconductor by a tunnel coupling of varying strength. At absolute zero temperature and for weak coupling, we find that the scattering states of the interferometer are decohered by Andreev reflection, a nontrivial manifestation of the proximity effect analogous to DSW decoherence from the event horizon of a black hole. However, for increasing coupling strength to the superconductor, we find a reemergence of coherence via resonant tunneling through Andreev bound states. This suggests the existence of an analogue gravitational phenomenon wherein transmission mediated by virtual Hawking radiation leads to a reemergence of coherence in an interferometer placed within a few Compton wavelengths of a black hole's event horizon.

We present a theory of the Josephson current in superconductor-normal metal-superconductor (SNS) junctions in the presence of generic spin-dependent fields, such as spin-orbit coupling (SOC), Zeeman fields, and altermagnetism. We consider systems with arbitrary disorder strength, going beyond the usual diffusive and ballistic approximations. Using the linearized quasiclassical Eilenberger equation, we derive a compact expression for the Josephson current, which is then applied to various situations of experimental interest. First, we investigate the evolution of the Josephson critical current in an applied magnetic field in the presence of Rashba and Dresselhaus SOC, and discuss how this dependence can be used to probe SOC in the junction. We then study the anomalous Josephson ($\varphi_0$) effect in systems with Rashba SOC and show that it remains robust over a wide range of disorder strength, and can even be enhanced by moderate disorder in sufficiently long junctions. Finally, we investigate the Josephson current in disordered junctions with altermagnets, and show how the $0$-$\pi$ transition in such systems is suppressed by disorder. Our results may be useful for describing experimental setups with high-mobility samples, which nevertheless always contain some amount of disorder, and where neither purely ballistic nor diffusive approximations are adequate.