Laboratory for Digitalisation — Prof. Dr. Wolfgang Mauerer

The partners of the TAQO-PAM project held their 6th cosortium meeting at Eviden in the beautiful city of Tübingen to exchange ideas and discuss the results of the last 6 months. Hila Safi, Maja Franz, Lukas Schmidbauer, Simon Thelen and Tom Krüger presented their latest results to the consortium.

Dr. Hans-Peter Nollert from the university of Tübingen gave a great talk on the origins of Eviden and on visualizations of special and general relativity. After some great food in the "Wurstküche", we went on a city tour as the final event of the day where we did not allow the rain to dampen our mood.

At this year's Linux Plumbers Conference, our PhD Student Benno Bielmeier gave a talk on his work on probabilistic real-time analyses and presented it to a broader audience. With his techniques, Benno tries to probabilistically predict real-time behaviour of complex software systems. His talk met high interest of Linux Kernel developers and ended in a fruitful discussion with core kernel developers. Congrats, Benno!

Abstract Ensuring temporal correctness of real-time systems is challenging. The level of difficulty is determined by the complexity of hardware, software, and their interaction. Real-time analysis on modern complex hardware platforms with modern complex software ecosystems, such as the Linux kernel with its userland, is hard or almost impossible with traditional methods like formal verification or real-time calculus. We need new techniques and methodologies to analyse real-time behaviour and validate real-time requirements.

In this talk, we present a toolkit designed to evaluate the probabilistic Worst-Case Execution Time (pWCET) of real-time Linux systems. It utilises a hybrid combination of traditional measurement-based and model-based techniques to derive execution time distributions considering variability and uncertainty in real-time tasks. This approach provides assessment of execution time bounds and supports engineers to achieve fast and robust temporal prediction of their real-time environments.

Our framework models runtime behaviour and predicts WCET in a streamlined four-phase process: (1) model relevant aspects of the system as finite automaton, (2) instrument the system and measure latencies within the model, (3) generate a stochastic model based on semi-Markov chains, and (4) calculate pWCET via extreme value statistics. This method is applicable across system context boundaries without being tied to specific platforms, infrastructure or tracing tools.

The framework requires injecting tracepoints to generate a lightweight sequence of timestamped events. This can be done by existing Linux tracing mechanisms, for instance, BPF or ftrace. Benefits include significantly reduced WCET measurement duration from days to minutes, dramatically accelerating development cycles for open-source systems with frequent code updates like Linux. This efficiency doesn't compromise accuracy; our hybrid approach ensures robust temporal predictions, enabling developers to quickly assess real-time implications of changes and maintain system performance.

In our talk, we outline the steps taken towards this new evaluation method and discuss the limitations and potential impacts on the development process. We invite interaction from the community to discuss the benefits and limitations of this approach. Our goal is to refine this toolkit to enhance its utility for Linux kernel developers and maintainers, ultimately contributing to a more efficient and effective development process for real-time systems.

For one final time, the QLindA consortium has met at OTH Regensburg, to review results and milestones achieved during the project's over three-year lifespan.

These milestones encompass a broad selection of publications on quantum machine learning for industrial applications, jointly organised workshops at the IEEE Conference on Quantum Computing and Engineering, and an extensive software library, among others.

Fitting to the occasion, a beer barrel was opened later in the evening, to properly celebrate the project's conclusion. Prost!

We are happy that all our full paper submissions to IEEE QCE, one of the leading quantum computing conferences, have been accepted:

• Maniraman Periyasamy, Axel Plinge, Christopher Mutschler, Daniel D. Scherer, Wolfgang Mauerer: Guided-SPSA: Simultaneous Perturbation Stochastic Approximation assisted by the Parameter Shift Rule
• Maja Franz, Tobias Winker, Sven Groppe, Wolfgang Mauerer: Hype or Heuristic? Quantum Reinforcement Learning for Join Order Optimisation

As always, it was a joy to work with our collaboration partners at Fraunhofer IIS and the University of Lübeck. Congratulations, Maja Franz and Maniraman Periyasamy!

Abstract The study of variational quantum algorithms (VQCs) has received significant attention from the quantum computing community in recent years. These hybrid algorithms, utilizing both classical and quantum components, are well-suited for noisy intermediate-scale quantum devices. Though estimating exact gradients using the parameter-shift rule to optimize the VQCs is realizable in NISQ devices, they do not scale well for larger problem sizes. The computational complexity, in terms of the number of circuit evaluations required for gradient estimation by the parameter-shift rule, scales linearly with the number of parameters in VQCs. On the other hand, techniques that approximate the gradients of the VQCs, such as the simultaneous perturbation stochastic approximation (SPSA), do not scale with the number of parameters but struggle with instability and often attain suboptimal solutions. In this work, we introduce a novel gradient estimation approach called Guided-SPSA, which meaningfully combines the parameter-shift rule and SPSA-based gradient approximation. The GuidedSPSA results in a 15% to 25% reduction in the number of circuit evaluations required during training for a similar or better optimality of the solution found compared to the parameter-shift rule. The Guided-SPSA outperforms standard SPSA in all scenarios and outperforms the parameter-shift rule in scenarios such as suboptimal initialization of the parameters. We demonstrate numerically the performance of Guided-SPSA on different paradigms of quantum machine learning

Abstract Identifying optimal join orders (JOs) stands out as a key challenge in database research and engineering. Owing to the large search space, established classical methods rely on approximations and heuristics. Recent efforts have successfully explored reinforcement learning (RL) for JO. Likewise, quantum versions of RL have received considerable scientific attention. Yet, it is an open question if they can achieve sustainable, overall practical advantages with improved quantum processors. In this paper, we present a novel approach that uses quantum reinforcement learning (QRL) for JO based on a hybrid variational quantum ansatz. It is able to handle general bushy join trees instead of resorting to simpler left-deep variants as compared to approaches based on quantum(-inspired) optimisation, yet requires multiple orders of magnitudes fewer qubits, which is a scarce resource even for post-NISQ systems. Despite moderate circuit depth, the ansatz exceeds current NISQ capabilities, which requires an evaluation by numerical simulations. While QRL may not significantly outperform classical approaches in solving the JO problem with respect to result quality (albeit we see parity), we find a drastic reduction in required trainable parameters. This benefits practically relevant aspects ranging from shorter training times compared to classical RL, less involved classical optimisation passes, or better use of available training data, and fits data-stream and low-latency processing scenarios. Our comprehensive evaluation and careful discussion delivers a balanced perspective on possible practical quantum advantage, provides insights for future systemic approaches, and allows for quantitatively assessing trade-offs of quantum approaches for one of the most crucial problems of database management systems.

Multiple contributions to IEEE QCE, IEEE QSW and ACM SIGMOD conferences

We are happy that a whole lot of submissions have been met with favourable response by reviewers recently:

• Quantum Data Encoding Patterns and their Consequences at the QDSM workshop at ACM SIGMOD by Martin Gogeißl, Hila Safi, and Wolfgang Mauerer
• Polynomial Reduction Methods and their Impact on QAOA Circuits at IEEE QSW by Lukas Schmidbauer and Wolfgang Mauerer, together with Karen Wintersberger (Siemens Technology) and Elisabeth Lobe (DLR)
• QCEDA: Using Quantum Computers for EDA at SAMOS'24, together with Matthias Jung (Uni Würzburg), Sven O. Krumke (RPTU Kaiserslautern), Christoph Schroth (Fraunhofer IESE), and Elisabeth Lobe (DLR)
• The second edition of the QML workshop at IEEE QCE, together with Daniel Hein (Siemens Technology)
• Our tutorial on quantum annealing for database optimisation at IEEE QCE'24, together with many colleagues from Lübeck and Helsinki, right from the leading places for research on quantum data management.

Thanks to all the involved group members and collaborators for the hard and exciting work!

Joint contribution to the 27th International Conference on Computing in High Energy & Nuclear Physics (CHEP) by Maja Franz, Manuel Schönberger and Wolfgang Mauerer, together with international partners:

• Melvin Stobl, Eileen Kuehn and Achim Streit (Karlsruhe Institute of Technology)
• Pia Zurita (Complutense University of Madrid, Spain)
• Markus Diefenthaler (Jefferson Lab, USA)

Abstract
Noisy intermediate-scale quantum (NISQ) computers, while limited by imperfections and small scale, hold promise for near-term quantum advantages in nuclear and high-energy physics (NHEP) when coupled with co-designed quantum algorithms and special-purpose quantum processing units. Developing co-design approaches is essential for near-term usability, but inherent challenges exist due to the fundamental properties of NISQ algorithms. In this contribution we therefore investigate the core algorithms, which can solve optimisation problems via the abstraction layer of a quadratic Ising model or general unconstrained binary optimisation problems (QUBO), namely quantum annealing (QA) and the quantum approximate optimisation algorithm (QAOA). Applications in NHEP utilising QUBO formulations range from particle track reconstruction, over job scheduling on computing clusters to experimental control. While QA and QAOA do not inherently imply quantum advantage, QA runtime for specific problems can be determined based on the physical properties of the underlying Hamiltonian, albeit it is a computationally hard problem itself.

Our primary focus is on two key areas: Firstly, we estimate runtimes and scalability for common NHEP problems addressed via QUBO formulations by identifying minimum energy solutions of intermediate Hamiltonian operators encountered during the annealing process. Secondly, we investigate how the classical parameter space in the QAOA, together with approximation techniques such as a Fourier-analysis based heuristic, proposed by Zhou et al. (2018), can help to achieve (future) quantum advantage, considering a trade-off between computational complexity and solution quality. Our computational analysis of seminal optimisation problems suggests that only lower frequency components in the parameter space are of significance for deriving reasonable annealing schedules, indicating that heuristics can offer improvements in resource requirements, while still yielding near-optimal results.

Wolfgang Mauerer, Ralf Ramsauer, Petra Eichenseher and Simon Thelen, together with Prof. Dr. Jürgen Mottok (LaS³, Faculty of Electrical and Information Technologies), paid a visit to MuQuaNet at its site at the University of the Bundeswehr Munich. We are proud to take part in Bavarian research regarding quantum cryptography with our own brand-new quantum key distribution system and are looking forward to opportunities to deepen our relationship with UniBW in the future.

In a prestigous event hosted by LfD, Bavarian State Minister for Science and Arts, Markus Blume, inaugurated the OTH's new quantum key distribution system provided by "Quantum Optics Jena" and funded by "Hightech Agenda Bayern". The system will play an important role in future cross-faculty efforts to integrate quantum cryptography into education, science and industry.

The event featured many key players from the Bavarian quantum science and industry commmunity, including Prof. Dr. Rudolf Gross from Munich Quantum Valley, Dr. Nils gentschen Felde from MuQuaNet, Prof. Dr. Christoph Marquardt from FAU, Laura Schulz from LRZ, Dr. Bettina Heim from OHB, Dr. Sebastian Luber from Infineon, Dr. Christoph Niedermeier from Siemens, Prof. Dr. Helena Liebelt from THD, Dr. Peter Eder from IQM, Dr. Andreas Böhm from Bayern Innovativ, Theresa Schreyer and Imran Khan from Keequant.

The LfD hosted an international, interdisciplinary exchange on quantum computing for nuclear and high-energy physics to discuss challenges and applications.

Guests from the USA, UK, Spain and Germany participated enthusiastically in the workshop and exchanged ideas on the latest advances in quantum computing and quantum machine learning.

We are thrilled to actively contribute to these pioneering efforts!

Markus Schottenhammer und Andreas Fellner verteigigen erfolgreich ihre Bachelorarbeiten: "Automatisierte Übungserfassung und Wiederholungserkennung mithilfe einer Smartwatch" und "Vergleich von Variationalen Quantenschaltkreis-Strukturen für Quanten-Reinforcement Learning". Glückwunsch an Beide!

Vincent Eichenseher successfully defends his Bachelor Thesis "Comparative Analysis of Parameter Selection Heuristics for the Quantum Approximate Optimisation Algorithm". Congrats, Vincent!

Lukas Schmidbauer has joined the team as doctoral student in the field of quantum computing, contributing to the TAQO-PAM project. Welcome, Lukas!

Simon Thelen has joined the team as doctoral student in the field of quantum computing, contributing to the TAQO-PAM project. Welcome, Simon!