Incremental advances in semiconductor technology of the past decades led to unprecedented miniaturization of optoelectronic integrated circuits, which now use billions of transistors, each containing only hundreds of atoms. However, these most sophisticated devices still rely on collective phenomena such as electric currents and light beams. These classical concepts are limited by atomic-scale effects and allow no further progress through miniaturization. Overcoming this bottleneck, would require a new generation of devices where atomic scale effects are no longer an obstacle but are used as a resource to build circuits through precise placement of individual atoms while exploiting quantum effects to boost information storage and processing capacity. Recent innovations in semiconductor material science and technology offer new routes to atomic scale miniaturisation. This project relies on a new type of semiconductor quantum dots, which are tiny semiconductor crystals consisting of only a few thousand atoms. A comprehensive program of material development and experimental physics studies will seek to demonstrate quantum information storage and processing with nuclear magnetic states of individual atoms incorporated into a quantum dot. The broad goal of this proposal is to understand fundamental phenomena and develop material technologies that will stimulate and guide the transition from existing classical digital chips to future devices, which will eventually use every individual atom of a semiconductor crystal as a resource to build integrated circuits with Avogadro-scale number of elementary units and unprecedented information processing power and energy efficiency.

Engineered nanoscale systems that provide access to the quantum properties of matter are heralding a revolution in physics and technology. Control over single quantum objects, such as a single electron or photon, and over interactions between them provides the means to engineer the correlations that make quantum technologies a revolutionary advance over their current counterparts. An interface between a stationary matter and a flying optical quantum bit (qubit) is a fundamental building block of the inter-connects that will make quantum technologies useful on a large scale. Solid-state devices have shown strongly coupled light-matter interfaces, efficient light collection, and quantum control of coherent matter nodes. Progress on fabrication techniques to enhance spin and optical coherence properties, combined with important theoretical efforts on modelling complex environments, have yielded significant gains in these areas. Indeed, recent demonstrations using optically addressable spins in semiconductors include a loophole-free test of Bell's inequalities, the generation of photonic states involved in measurement-based quantum computation, and the realisation of quantum internet primitives. Alongside ultracold atoms and superconducting circuits, such optically active solid-state platforms provide developments with distinct long-term advantages due to their ease of integration with combined classical optical and electrical elements. This project will put together a next-generation solid-state quantum networking node that combines the latest developments in the quantum optical research community -- optical device integration, all-optical electron spin control, and nuclear spin coherence and control -- to deliver a platform that outperforms other candidate technologies on the combined metrics of optical coherence and efficiency, quantum bit control, and quantum memory lifetime. This proposal consists of realising this combination by leveraging two recent breakthroughs in a system already known as the best single photon source - III-V semiconductor quantum dots: (1) open optical microcavities as a versatile interface to reach a strong light-matter coupling and high collection efficiency, and (2) strain-free GaAs quantum dots, as host for a coherent matter quantum bit, and on which preliminary measurements indicate a two orders of magnitude improvement in coherence time over the state of the art (InAs quantum dots). As a first major benchmark and the major deliverable of this proposal, a deterministic quantum gate will be performed between two photon qubits, leveraging the optical and spin coherence of this new generation of quantum dots. This proposal aims to reach beyond 1MHz entanglement rate between two photon qubits while achieving a few-percent error rate - a more than four orders of magnitude improvement of the rate-fidelity product over previous attempts in the optical domain. This will serve as a proof-of-concept to establish this platform as the optimal choice for investment towards large-scale arrays of quantum optical devices. Finally, developing this GaAs quantum dot platform promises to equip the leading commercial single-photon emitters with a long-lived nuclear-spin memory, the missing piece for this otherwise exquisite photonics platform. This addition would allow the demonstration of long-lived entanglement across distant quantum nodes, a crucial step en route to a quantum internet where such entanglement can be used as a resource for communication and computation.

1) Wider research context / theoretical framework This project aims at the development of a novel framework for high-order discretization of partial differential equations on general domains. The latter pose challenges related to their topology and in particular at the vicinity of, so called, extraordinary vertices where smoothness requirements and superior approximation power are paramount for efficient simulations. 2) Hypotheses/research questions /objectives We focus on the paradigm of isogeometric analysis that uses spline functions for design and analysis on non-linear geometries. We propose a framework of geometrically continuous splines called RFF-Splines (Refinable FreeForm Splines) that shall enable numerical schemes for topologically unrestricted design and analysis. 3) Approach/methods The project goes all the way from the theoretical construction to its algorithmic derivation and the efficient implementation in C++, as well as experimental evaluation in demanding applications involving high order partial differential equations. 4) Level of originality / innovation The novelty of the construction stems from the efficient construction of the basis functions (notably for evaluation and numerical integration), adaptivity by local refinement (via a truncation mechanism) as well as the good approximation power, supported by theoretical results. The idea of RFF-Splines is inspired from the work of Hartmut Prautzsch and is based on composing polynomial mappings with spline parameterizations. 5) Primary researchers involved The project involves Bert Juettler (JKU Linz), Angelos Mantzaflaris (Researcher at INRIA), Bernard Mourrain and Regis Duvigneau (Research directors at INRIA), and two PhD students (one at JKU and one at INRIA).

Engineered nanoscale systems that provide access to the quantum properties of matter are heralding a revolution in physics and technology. Control over single quantum objects, such as a single electron or photon, and over interactions between them provides the means to engineer the correlations that make quantum technologies a revolutionary advance over their current counterparts. An interface between a stationary matter and a flying optical quantum bit (qubit) is a fundamental building block of the inter-connects that will make quantum technologies useful on a large scale. Solid-state devices have shown strongly coupled light-matter interfaces, efficient light collection, and quantum control of coherent matter nodes. Progress on fabrication techniques to enhance spin and optical coherence properties, combined with important theoretical efforts on modelling complex environments, have yielded significant gains in these areas. Indeed, recent demonstrations using optically addressable spins in semiconductors include a loophole-free test of Bell's inequalities, the generation of photonic states involved in measurement-based quantum computation, and the realisation of quantum internet primitives. Alongside ultracold atoms and superconducting circuits, such optically active solid-state platforms provide developments with distinct long-term advantages due to their ease of integration with combined classical optical and electrical elements. This project will put together a next-generation solid-state quantum networking node that combines the latest developments in the quantum optical research community -- optical device integration, all-optical electron spin control, and nuclear spin coherence and control -- to deliver a platform that outperforms other candidate technologies on the combined metrics of optical coherence and efficiency, quantum bit control, and quantum memory lifetime. This proposal consists of realising this combination by leveraging two recent breakthroughs in a system already known as the best single photon source - III-V semiconductor quantum dots: (1) open optical microcavities as a versatile interface to reach a strong light-matter coupling and high collection efficiency, and (2) strain-free GaAs quantum dots, as host for a coherent matter quantum bit, and on which preliminary measurements indicate a two orders of magnitude improvement in coherence time over the state of the art (InAs quantum dots). As a first major benchmark and the major deliverable of this proposal, a deterministic quantum gate will be performed between two photon qubits, leveraging the optical and spin coherence of this new generation of quantum dots. This proposal aims to reach beyond 1MHz entanglement rate between two photon qubits while achieving a few-percent error rate - a more than four orders of magnitude improvement of the rate-fidelity product over previous attempts in the optical domain. This will serve as a proof-of-concept to establish this platform as the optimal choice for investment towards large-scale arrays of quantum optical devices. Finally, developing this GaAs quantum dot platform promises to equip the leading commercial single-photon emitters with a long-lived nuclear-spin memory, the missing piece for this otherwise exquisite photonics platform. This addition would allow the demonstration of long-lived entanglement across distant quantum nodes, a crucial step en route to a quantum internet where such entanglement can be used as a resource for communication and computation.

INDEX will study efficient incremental solutions to combinatorial optimisation problems occurring in design of computer experiments. Modern industrial processes often resort to simulation models of huge computational costs. Use of the original numerical codes for engineering tasks such as design optimisation and performance assessment, which require an intensive exploration of the model input space, would then require unrealistic amount of time. The current trend is to substitute the original numerical codes by a surrogate model of much lesser complexity, often a semi-parametric interpolator of a finite set of its outputs. The quality of the surrogate model depends on the set of simulation inputs (the design) used for this construction, and, obviously, it increases with design size. Classical approaches to design of experiments consider the design size N as a fixed parameter and try to optimise the information in the overall set of N points. However, in many situations the model simulations are progressively integrated, and a decision to stop the learning process is done on-line, based either on the estimated quality of the surrogate model already built or, more pragmatically, because the available (time, cost) budget has been totally consumed. In this context, it is important that the order of execution of the design points be well chosen, such that for all n