In recent years, the field of quantum technologies has experienced significant growth. During this expansion, quantum simulators have emerged as one of the most experimentally advanced platforms. These are devices that can simulate highly complex quantum systems, and are an area in which Europe currently holds a competitive advantage. There is a growing consensus among physicists that quantum simulators have achieved a so-called quantum advantage. However, these results have received considerably less attention and scrutiny than similar claims made for digital quantum computers. TouQan aims to bridge the gap in our understanding of potential quantum advantages in quantum simulators. We do this by engaging in a “cat-and-mouse” investigation, in which each of the objectives aims to narrow down the scope of the others. Firstly, we will advance our knowledge of the computational power of simulators from a mathematically rigorous perspective and will find ways of characterizing it, including the impact of hardware noise. Secondly, we will examine under which conditions classical computers can effectively simulate quantum simulators to narrow down when they do not offer significant advantages. By doing so, a clearer picture of what these devices can achieve will emerge, attracting a wider community of researchers to quantum simulators, and strengthening Europe's position in the sector. The interdisciplinary nature of this project will require the use and development of advanced tools at the intersection of computer science, physics, and mathematical physics. Our consortium comprises five ambitious early-career researchers with solid track records and based in various European countries. This collaborative effort will foster increased cooperation among European nations on a timely topic, ultimately bolstering the development of quantum simulators and enhancing our understanding of their computational power, and in particular of how they offer the widely-sought quantum advantage.

Zweck des Vorhabens ist die interdisziplinäre Forschung in den Bereichen Quantenphysik, Mikrosystemtechnik, Hochfrequenztechnik und Informatik, um die notwendigen Technologien für die Entwicklung und den Einsatz von Quantum Computing aufzubauen. Primäres Ziel ist die Durchführung von Forschungsprojekten im Bereich Quantencomputin. Ein weiteres zentrales Ziel ist die Ausbildung des wissenschaftlichen Nachwuchses (Promovierende und Postdoktorand:innen) im Bereich Quantencomputing, um dringend benötigtes Personal zur Stärkung des „Ökosystems Quantencomputing “ in Hamburg bereitzustellen.

In Quantencomputern wird Information in Quantenbits gespeichert und verarbeitet. Quantenbits können, im Gegensatz zu klassischen Bits, gleichzeitig die Werte 0 und 1 annehmen. Diese Gleichzeitigkeit, die sogenannte Quantenparallelität, ist ein wesentliches Merkmal von Quantencomputern und ermöglicht ihnen die effiziente Lösung von komplexen Problemen, welche aufgrund ihrer Skalierung auch für die besten Bit‐basierten Supercomputer praktisch unlösbar bleiben werden. Tatsächlich wurde die Lösung solcher Probleme bereits in existierenden Quantencomputern demonstriert. Diese sind jedoch für industrielle und wissenschaftliche Anwendungen noch nicht ausreichend leistungsfähig. Das MIQRO‐Projekt wird einen modularen Quantencomputer entwickeln, aufgebaut aus „Quanten‐Kernen“, welche gespeicherte atomare Ionen als Quantenbits verwenden. Die in diesen mit hoher Funktionalität ausgestatteten Quanten‐Kernen ausgeführten quantenlogischen Operationen werden durch Hochfrequenz (HF)‐Wellen kontrolliert. Dies wird durch Magnetic Gradient Induced Coupling, kurz MAGIC, ermöglicht. Das MAGIC-Konzept unterscheidet sich von anderen Ansätzen durch perfekt reproduzierbare Qubits, stark reduzierte Kühlanforderungen und sehr gut integrierbare Hochfrequenzelektronik für die Steuerung der Qubits. Darüber hinaus wird die gleichzeitige Kopplung vieler Qubits in einem Quantenkern bei gleichzeitig unerreicht kleinem Übersprechen (fehlerhafte Veränderung nicht‐adressierter Qubits) zwischen den Qubits, Quantenalgorithmen beschleunigen. Die MAGIC‐Methode wird hier um neue leistungsfähige, mikrostrukturierte Ionenspeicher erweitert. Dies wird Quantengatter hoher Güte und quantenlogische Fehlerkorrektur ermöglichen und so entscheidend zur Skalierung von Quantenrechnern beitragen. Der in diesem Projekt entwickelte und betriebene Quantenkern stellt das Herzstück eines zukünftigen Ionen‐basierten, universellen Quantencomputers dar. Dieser Quantencomputer wird auf Tausend Qubits skalierbar sein und damit vielfältigen industriellen und akademischen Anwendungen den Weg bereiten.

Quantum sciences are currently enjoying a large amount of attention including heavy research investments by governments as well as commercial companies. A central promise is that classical computations will be outperformed by using quantum resources. This has potential applications in numerous fields such as in quantum chemistry, optimization, and artificial intelligence. An important milestone for achieving such ambitious aims is the demonstration of quantum supremacy: this means to solve some problem by using quantum capabilities that cannot practically be solved otherwise. It is to be expected that quantum supremacy will be announced in the near future. However, what would it actually tell us? A convincing demonstration of quantum supremacy would show that quantum computers have reached a level where they might actually become useful. But, if a quantum device cannot practically be simulated how can one make sure that its outcome is correct? In particular, how can a skeptic be convinced of quantum supremacy? Many of the proposed quantum supremacy demonstrations –specifically quantum sampling experiments– have the caveat that there is no convincing practical test of whether or not they have been correctly solved. Two tasks are utterly important for the development of trusted quantum devices: (i) the verification of their functioning as a whole and (ii) the precise characterization of their single components; the latter being crucial for their development itself. There is a range of methods targeted at these two and also intermediate tasks. This includes quantum state verification, quantum process validation (such as randomized benchmarking), certain classical simulation techniques and quantum tomography. However, experimentally practical methods that also feature precise theoretical performance guarantees are still rare. Now is the right time to close this gap. On the one hand, there are new powerful mathematical techniques and results. They range from vector and operator concentration inequalities, over tensor reconstruction, non-convex optimization, and new developments in machine learning to new precisely controlled sampling methods in quantum information theory. On the other hand, the precisely controlled quantum systems have become so large that new efficient data processing techniques are required. The proposed Emmy-Noether group will open the investigation of worst-case errors in the verification of quantum dynamics, provide practical quantum process tomography schemes with theoretical guarantees, provide the first systematic investigation of the role of temporal noise correlations in quantum processes, and investigate the role of noise for the complexity of classical simulations of complex quantum systems. This project aims at the development of methods that are practical and mathematically rigorous at the same time, as desirable in the regime of high complexity.

Quantum sciences are currently enjoying a large amount of attention including heavy research investments by governments as well as commercial companies. A central promise is that classical computations will be outperformed by using quantum resources. This has potential applications in numerous fields such as in quantum chemistry, optimization, and artificial intelligence. An important milestone for achieving such ambitious aims is the demonstration of quantum supremacy: this means to solve some problem by using quantum capabilities that cannot practically be solved otherwise. It is to be expected that quantum supremacy will be announced in the near future. However, what would it actually tell us? A convincing demonstration of quantum supremacy would show that quantum computers have reached a level where they might actually become useful. But, if a quantum device cannot practically be simulated how can one make sure that its outcome is correct? In particular, how can a skeptic be convinced of quantum supremacy? Many of the proposed quantum supremacy demonstrations –specifically quantum sampling experiments– have the caveat that there is no convincing practical test of whether or not they have been correctly solved. Two tasks are utterly important for the development of trusted quantum devices: (i) the verification of their functioning as a whole and (ii) the precise characterization of their single components; the latter being crucial for their development itself. There is a range of methods targeted at these two and also intermediate tasks. This includes quantum state verification, quantum process validation (such as randomized benchmarking), certain classical simulation techniques and quantum tomography. However, experimentally practical methods that also feature precise theoretical performance guarantees are still rare. Now is the right time to close this gap. On the one hand, there are new powerful mathematical techniques and results. They range from vector and operator concentration inequalities, over tensor reconstruction, non-convex optimization, and new developments in machine learning to new precisely controlled sampling methods in quantum information theory. On the other hand, the precisely controlled quantum systems have become so large that new efficient data processing techniques are required. The proposed Emmy-Noether group will open the investigation of worst-case errors in the verification of quantum dynamics, provide practical quantum process tomography schemes with theoretical guarantees, provide the first systematic investigation of the role of temporal noise correlations in quantum processes, and investigate the role of noise for the complexity of classical simulations of complex quantum systems. This project aims at the development of methods that are practical and mathematically rigorous at the same time, as desirable in the regime of high complexity.