Quantum computing (QC) is a new and disruptive technology with large economic potential especially in application and downstream value creation stages. Hence, it is important for an economy to understand the current implementation state and to know the ecosystem to support the successful industrial application of this technology. Regularly identifying potential areas of improvement and then defining appropriate actions is necessary to ensure a leading position. Therefore, the Quantum Technology and Application Consortium (QUTAC) has developed a Key Performance Indicator (KPI) framework consisting of 24 KPIs that represent a country’s performance in applying QC. Detailed measurement guidelines and clear data sources ensure transparency of measurement, reproducibility of KPI values and comparability over time. An aggregation method allows summarizing the results of all KPIs. Thus, it is possible to assess the performance of each stakeholder involved and to calculate a single composite indicator that represents the country’s performance. The KPI framework can be adapted to any country and enables the comparison of the performance of different countries. It is a proposal for standardizing the evaluation of QC and its ecosystem on a national level. Thus, strengths and weaknesses can be identified and measurements for improvement derived. The paper highlights the development of the framework, its main features and the application of the framework to Germany. Based on the results, we will discuss the current state of QC application in Germany and make possible suggestions for improvement.

This is the second paper in a series of papers providing an overview of different quantum computing hardware platforms from an industrial end-user perspective. It follows our first paper on neutral-atom quantum computing. In the present paper, we provide a survey on the current state-of-the-art in trapped-ion quantum computing, taking up again the perspective of an industrial end-user. To this end, our paper covers, on the one hand, a comprehensive introduction to the physical foundations and mechanisms that play an important role in operating a trapped-ion quantum computer. On the other hand, we provide an overview of the key performance metrics that best describe and characterise such a device's current computing capability. These metrics encompass performance indicators such as qubit numbers, gate times and errors, native gate sets, qubit stability and scalability as well as considerations regarding the general qubit types and trap architectures. In order to ensure that these metrics reflect the current state of trapped-ion quantum computing as accurate as possible, they have been obtained by both an extensive review of recent literature and, more importantly, from discussions with various quantum hardware vendors in the field. We combine these factors and provide - again from an industrial end-user perspective - an overview of what is currently possible with trapped-ion quantum computers, which algorithms and problems are especially suitable for this platform, what are the relevant end-to-end wall clock times for calculations, and what might be possible with future fault-tolerant trapped-ion quantum computers.

We present an industrial end-user perspective on the current state of quantum computing hardware for one specific technological approach, the neutral atom platform. Our aim is to assist developers in understanding the impact of the specific properties of these devices on the effectiveness of algorithm execution. Based on discussions with different vendors and recent literature, we discuss the performance data of the neutral atom platform. Specifically, we focus on the physical qubit architecture, which affects state preparation, qubit-to-qubit connectivity, gate fidelities, native gate instruction set, and individual qubit stability. These factors determine both the quantum-part execution time and the end-to-end wall clock time relevant for end-users, but also the ability to perform fault-tolerant quantum computation in the future. We end with an overview of which applications have been shown to be well suited for the peculiar properties of neutral atom-based quantum computers.

Quantum computing promises to overcome computational limitations with better and faster solutions for optimization, simulation, and machine learning problems. Europe and Germany are in the process of successfully establishing research and funding programs with the objective to advance the technology’s ecosystem and industrialization, thereby ensuring digital sovereignty, security, and competitiveness. Such an ecosystem comprises hardware/software solution providers, system integrators, and users from research institutions, start-ups, and industry. The vision of the Quantum Technology and Application Consortium (QUTAC) is to establish and advance the quantum computing ecosystem, supporting the ambitious goals of the German government and various research programs. QUTAC is comprised of ten members representing different industries, in particular automotive manufacturing, chemical and pharmaceutical production, insurance, and technology. In this paper, we survey the current state of quantum computing in these sectors as well as the aerospace industry and identify the contributions of QUTAC to the ecosystem. We propose an application-centric approach for the industrialization of the technology based on proven business impact. This paper identifies 24 different use cases. By formalizing high-value use cases into well-described reference problems and benchmarks, we will guide technological progress and eventually commercialization. Our results will be beneficial to all ecosystem participants, including suppliers, system integrators, software developers, users, policymakers, funding program managers, and investors.

Magnetoresistive sensors based on giant magnetoresistance (GMR) or tunnel magnetoresistance (TMR) play a major role towards the miniaturization in the industrial society. Typically, spin-valve-type magnetoresistive sensors are embedded in a Wheatstone bridge configuration with rectangular, meander-like or elliptically shaped thin film elements. Such elements usually switch via multi-domain, C- or S-shaped magnetization states and, therefore, often exhibit an open non-linear hysteresis curve. Linearity and hysteretic effects are key features in the improvement of such sensors. We will present a different approach by using circularly shaped elements exhibiting a different magnetization state of a magnetic vortex [1]. This is one of the fundamental magnetization ground states occurring in disk-shaped thin film elements and is characterized by minimization of the demagnetizing energy at the expense of exchange energy. Experimental data were generated on electrically contacted GMR and TMR disks which were fabricated by optical lithography. The following advantages will be discussed and compared to standard elliptical sensor elements. (a) The vortex state shows essentially no hysteresis in the minor loop. (b) Since the vortex nucleation happens prior to the zero field, the M(H=0)=0 crossing is independent of history. (c) The critical fields can be easily controlled by the element geometry. (d) The noise is low. All characteristic experimental values have been determined in dependence of free layer thickness, disk diameter and temperature. These findings are discussed in the frame of the semi-analytical rigid-vortex-model [2] and micromagnetic simulations. The financial support by the Austrian Federal Ministry of Science, Research and Economy and the Christian Doppler Research Association in Austria is gratefully acknowledged. [1] D. Suess, A. Bachleitner-Hofmann, A. Satz, H. Weitensfelder, C. Vogler, F. Bruckner, C. Abert, K. Prügl, J. Zimmer, C. Huber, S. Luber, W. Raberg, T. Schrefl, H. Brückl, „Topologically Protected Vortex Structures to Realize Low-Noise Magnetic Sensors with High Linear Range”, Nature Electronics 1, 362 (2018) [2] K. Y. Guslienko et al., “Magnetization reversal due to vortex nucleation, displacement, and annihilation in submicron ferromagnetic dot arrays”, Phys. Rev. B 65 (2001)

Magnetoresistive spin valve sensors based on the giant- (GMR) and tunnelling- (TMR) magnetoresisitve effect with a flux-closed vortex state free layer design are compared by means of sensitivity and low frequency noise. The vortex state free layer enables high saturation fields with negligible hysteresis, making it attractive for applications with a high dynamic range. The measured GMR devices comprise lower pink noise and better linearity in resistance but are less sensitive to external magnetic fields than TMR sensors. The results show a comparable detectivity at low frequencies and a better performance of the TMR minimum detectable field at frequencies in the white noise limit.

Micromagnetic sensors play a key role in a variety of industries, including the automotive industry, where they are used, for example, for speed and position detection. The adoption of emerging magnetoresistive sensor technology such as anisotropic magnetoresistance, giant magnetoresistance and tunnel magnetoresistance sensors is driven principally by their enhanced sensitivity and improved integration capabilities compared with conventional Hall effect sensors. At the heart of such sensors is a microstructured ferromagnetic thin-film element that transduces the magnetic signal, but these elements often exhibit a nonlinear hysteresis curve and the performance of the sensors is limited by magnetic noise. Here, we examine the origin of magnetic noise in magnetoresistive sensors and show that a topologically protected magnetic vortex state in the transducer element can be used to overcome these limitations. Using analytic and micromagnetic models, we find that the noise is due mainly to irreproducible magnetic switching of the transducer element at external fields that are close to the Stoner–Wohlfarth switching field. Then, using a flux-closed vortex configuration, we develop a giant magnetoresistance sensor layout that, compared to existing state-of-the-art sensors, has lower magnetic noise, a linear regime that is around an order of magnitude higher and negligible hysteresis.

Summary form only given. In this paper, we present a different approach by using circularly shaped elements exhibiting a different magnetization state. The magnetic vortex is one of the fundamental magnetization ground states occurring in disk-shaped thin film elements and is characterized by minimization of the demagnetizing energy at the expense of exchange energy. The state is described as free of hysteresis and planar stray-fields, and discussed as potential oscillator in spin-torque systems, memory bits and magnetic field sensors. In order to compare important parameters like resistance, magnetoresistance amplitude, sensitivity, hysteresis, critical fields like nucleation and annihilation fields in dependence on the free layer thickness and disk radius, single and arrays (10 and 1750 in number) of GMR disks have been fabricated by optical lithography and contacted.

Among the beyond-CMOS technologies, perpendicular Nano Magnetic Logic (pNML) is a promising candidate due to its low power consumption, its non-volatility and its monolithic 3D integrability, which makes it possible to integrate memory and logic into the same device by exploiting the interaction of bi-stable nanomagnets with perpendicular magnetic anisotropy. Logic computation and signal synchronization are achieved by focus ion beam irradiation and by pinning domain walls in magnetic notches. However, in realistic circuits, the information storage and their read-out are crucial issues, often ignored in the exploration of beyond-CMOS devices. In this paper we address these issues by experimentally demonstrating a pNML memory element, whose read and write operations can be controlled by two independent pulsed currents. Our results prove the correct behavior of the proposed structure that enables high density memory embedded in the logic plane of 3D-integrated pNML circuits.

Micromagnetic sensors play a major role towards the miniaturization in the industrial society. The adoption of new and emerging sensor technologies like anisotropic magnetoresistance (AMR), giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR) sensors are mainly driven by their integrability and enhanced sensitivity. At the core of such sensors, a microstructured ferromagnetic thin film element transduces the magnetic signal. Such elements usually switch via multi-domain, C- or S-shaped magnetization states and, therefore, often exhibit an open non-linear hysteresis curve. Linearity and hysteretic effects, as well as magnetic noise are key features in the improvement of such sensors. Here, we report on the physical origin of these disturbing factors and the inherent connection of noise and hysteresis. Critical noise sources are identified by means of analytic and micromagnetic models. The dominant noise source is due to irreproducible magnetic switching of the transducer element at external fields close to the Stoner Wohlfarth switching field. Furthermore, a solution is presented to overcome these limiting factors: a disruptive sensor design is proposed and analyzed which realizes a topologically protected magnetic vortex state in the transducer element. Compared to state of the art sensors the proposed sensor layout has negligible hysteresis, a linear regime about an order of magnitude higher and lower magnetic noise making the sensor ideal candidate for applications ranging from automotive industry to biological application.

Field strength sensors based on the AMR effect require field biasing concept to guarantee a unique signal characteristic. The exchange bias approach using a natural antiferromagnetic material is an advantageous possibility to provide a field bias to the sensor. PtMn exhibits a high thermal robustness and a high blocking temperature i.e. a good exchange bias coupling even at high temperatures. However, PtMn provokes a magnetically hysteretic behavior of the AMR layer. An antiferromagnetic interlayer coupling to an additionally introduced directly exchange bias coupled pinned layer significantly reduces the observed magnetic hysteresis. By adapting the interlayer coupling and the thickness of the pinned layer the hysteresis as well as the linear range of the sensor can be modified. The experimental findings will be qualitatively explained by a Stoner-Wohlfarth model.

We present a method to fabricate multiple metal nanogap electrodes of tailored width and distance in parallel, on the cleaved plane of a GaAs/AlGaAs heterostructure. The three-dimensional patterned structures are obtained by a combination of molecular-beam-epitaxial regrowth on a crystal facet, using the cleaved-edge-overgrowth (CEO) method, and subsequent wet selective etching and metallization steps. SEM and AFM studies reveal smooth and co-planar electrodes of width and distance of the order of 10 nm. Preliminary electrical characterization indicates electrical gap insulation in the 100 MΩ range with kΩ lead resistance. We propose our methodology to realize multiple electrode geometries that would allow investigation of the electrical conductivity of complex nanoscale objects such as branched organic molecules.

GaAs electrodes coated with hydrophobic, methyl-mercaptobiphenyl (CH3-MBP) monolayers exhibited an excellent electrochemical stability. We found that the interface resistance of the chemically functionalized GaAs shows linear relationships with electrolyte pH and bias potential in a reproducible manner. The impedance spectra measured in a wide frequency range ( f = 100 kHz to 50 mHz) are analyzed with several equivalent circuit models in a quantitative manner, and the pH sensitivity extrapolated from two linear relationships (35 mV pH(-1)) can be attributed to the absorption of the OH- ions on the hydrophobic surface.

A method of fabricating a pair of closely spaced metal electrodes on the cleaved plane of a GaAs/AlGaAs heterostructure (see image) is presented. These smooth, coplanar electrodes oppose each other over a predetermined distance of a few nanometers, continuously over their entire width of tens of micrometers. This structure may be used for the determination of the average electrical conductance of molecules.

Low lysine levels: The authors present a device (see picture) based on silicon-on-insulator (SOI) substrates that enables the detection of poly-L-lysine at concentrations of only 1 nM (80 ng mL−1).