Power grids require accurate power flow analysis and state estimation to ensure efficient energy distribution and stability. Traditional methods face challenges in solving the high-dimensional, linear equations involved, particularly as grids grow in complexity with the integration of renewable energy sources and dynamic demand patterns. Grid data is stored in large data structures and to optimize data-storage and -processing, these data structures can be ordered in a particular way. Once a good order is found for the data-structure of a particular grid, it can be used for all subsequent calculations over that grid. Finding this order is computationally challenging, and quantum computers may provide a solution for organizations like Alliander that are faced with scaling up their energy grids to meet future demands.

The Solution

n this project we developed a quantum algorithm for matrix reordering, known as qreorder. Finding the optimal matrix order is an NP-hard problem that can be phrased as a combinatorial optimization problem over graphs. This makes the problem suitable to be solved using a quantum annealer, but with an exponential overhead in the number of constraints and the required computational resources to solve it. To reduce the number of constraints for the quantum annealing formulation, we solved the optimization problem using “Benders Cuts”, which iteratively makes the problem formulation more complex until an optimal order is found. At each iteration of the optimization schedule, the quantum annealer is used. The solution is posted on our Quantumapplicationlab Github.

Diagram of the computational workflow for performing power flow analysis. The goal is to solve the equation Ax=b and this process can be optimized by reordering the matrix A, for which we developed a quantum algorithm.

The Benefits

Classical solutions to the problem of finding an optimal matrix order already make use of heuristic computational methods that sacrifice accuracy for speed. The goal in this project was to use quantum heuristics to find (near)optimal solutions, for small real-world energy grids, that could potentially allow for speed-ups with increasing problem sizes while leading to a higher accuracy than classical heuristics. We showed that, using classical pre-processing, we can find optimal orders for grid data of real-world energy grids in Alliander’s management with up to 700 different nodes.

The results of the project were presented at the 11th annual PowerWeb conference at TUDelft in November 2024, where colleagues demonstrated the following poster:

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Radiotherapy, a critical cancer treatment, relies on precise radiation dose planning to maximize effectiveness while minimizing harm to healthy tissue. Traditional methods for Fluence Map Optimization (FMO) struggle with computational complexity, especially as treatment plans involve more variables and higher voxel counts, a type of three-dimensional pixel. Since the optimization problem requires both minimizing damage done to healthy tissue and maximizing dose administered to target organs, there is not a single optimal plan, but rather a “Pareto front” of optimal plans. For organizations like Elekta and the UMC Utrecht, understanding novel computational tools like quantum computing is important for potentially improving the speed or accuracy with which radiotherapy plans are made.

The Solution

In this project the potential of quantum annealing for FMO was investigated. Quantum annealers explore complex optimization landscapes using principles of quantum mechanics, and research has demonstrated that they have the potential to do this faster than classical methods when the technology matures. Since the FMO problem involves solving a large optimization task, the use of quantum annealers is a good fit. The FMO problem is first reformulated into a QUBO (Quadratic Unconstrained Binary Optimization) format, enabling compatibility with annealing hardware. Simulated annealing (SA) serves as a practical benchmark for current quantum annealers, while hybrid solvers combine quantum and classical approaches for larger problem sizes. We solved several formulations of the FMO problem with varying complexities, adapting the number of beam angles, the beam resolution, the number of organs at risk and the number of voxels of the problem formulation. This allowed us to get a better grip on how the different problem variables impact the efficiency of a quantum solution.

Diagram of calculated dose to a planned target volume in a prostate, with doses computed using Simulated Annealing, over three radiation beam angles.

The Benefits

In this project, we demonstrated that a simple FMO problem for one organ at risk, consisting of three radiation beam angles can be solved using quantum annealing. We also demonstrated that more complex problem formulations involving multiple organs at risk can be solved using simulated annealing. Feasibility was established but claims about the scalability and benefits of the quantum solution require further research. Due to the simplified nature of the problem formulations that could be handled by a quantum annealer, and the rigor required for demonstrating clinical application, it was determined in this project that is too early for quantum computing to aid in improving FMO computations.

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Large water distribution system operators like Vitens are faced with network models that are intractable to simulate in their full scale in short time periods and must instead simulate smaller networks over larger time periods. These models are important for understanding e.g., pipe friction parameters, determining least-cost designs, finding leaks, developing digital twins and more.

Traditional methods may struggle with the complexity of predicting and managing water flow, especially under varying loading conditions and for large networks. The use of quantum computing may improve decision-making processes and enhance the development of water distribution resources.

The Quantum Solution

Quantum computing offers new approaches for WDN management by leveraging its ability to process complex optimization problems and simulate systems with high accuracy. Two different solutions were developed in this project. In the first, a quantum adaptation was made to the well-known Newton-Raphson algorithm, dubbed Quantum Newton-Raphson (QNR). In QNR one of three different quantum linear solvers can be used in a classical iterative modelling process. In the second solution, we worked towards a more concrete use-case of hydraulic modelling and developed a quantum annealing algorithm for water distribution network design, which finds the optimal combination of pipe-diameters when installing a new water distribution network.

Simulated annealing results for our Water Distribution Network design algorithm. On the x-axis, 5 different pairs of pipe diameters, with the left-most pair representing the known optimal design.

The Benefits

For QNR we found that the QUBO linear solver and Variational linear solvers performed the best, whereas the HHL linear solver required too large a qubit count to be feasible on the near-term. We performed accurate simulations of small 2-loop networks on quantum emulators, determining feasibility of our application. The implementation is found on our Github, here.  

Our quantum annealing algorithm for network design led to a highly complex annealing formulation, allowing us to solve networks of up to size 3 for using simulated annealing, the results are depicted in the above image. The implementation is also found on our Github, here.

This work is supported by the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme

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Breeding describes the process of selecting animals or plants with favorable characteristics that can be inherited to improve future generations and obtain higher yields, improved quality, disease resistance, and sustainability. To do this, characteristics (“phenotypes”) and DNA information (“genotypes”) of individuals are collected and subsequently used to estimate the expected performance of an offspring (“breeding value”). As modern breeding programs can contain millions of individuals and tens of thousands of genetic markers, this results in high computational demands.  Researchers, such as those at Wageningen University & Research (WUR), work on developing algorithms and applications for dealing with these challenges.

The Quantum Solution

To address these challenges, this research developed and explored together with WUR randomized algorithms for singular-value decompositions. By reducing the dimensionality of large genetic datasets, these methods speed up computational processes while preserving accuracy. A key component explored is the use of quantum-inspired sampling techniques to focus on retrieving the top 5% of individuals with the highest genetic merit, avoiding the inefficiency of estimating the genetic merit of the remaining 95% individuals. Tools like the truncated Singular Value Decomposition (SVD) and Halko’s randomized algorithms demonstrated significant potential in reducing computation times while maintaining acceptable accuracy.

The blue curve denotes the actual breeding values of specimens with the breeding values on the y-axis and on the ax-axis its position in ascending order. The red lines denote the sampled highest 5% breeding values using the quantum inspired algorithm.

The Benefits

The approach could offer major potential benefits for genomic selection. Dimensionality reduction techniques enable more efficient genomic predictions, optimizing resource use and reducing the time needed to identify individuals with high genetic merit. Early experiments validated that tools like Halko’s randomized SVD can accelerate computations while maintaining accuracy, making these methods particularly valuable for large-scale datasets, even without the use of quantum(-inspired) methods. By focusing computational efforts on high-value outcomes, quantum and quantum-inspired algorithms have the potential to enhance breeding programs, supporting greater food security, enhanced biodiversity conservation, and a more sustainable agricultural future.

This work is supported by the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme

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At Air France KLM over 7,000 employees work in shifts with different contract percentages, skill and authorization levels, etc. Efficiently scheduling all these employees becomes a complex combinatorial task. To solve it classically, Air France KLM simplifies the problem by designing both base rosters and personal rosters, reducing its efficiency.

Designing personal rosters directly would make the company adjustable in to a world in which it is extremely difficult to plan for a future that is constantly changing and while this task is classically intractable, quantum computing heuristics have shown potential to handle combinatorial problems effectively.

The Quantum Solution

e solution employs quantum annealing, a technique used to find the global minimum in a given function, revolutionizing rostering processes. This approach is particularly suited for solving optimization problems, which are common in complex scheduling tasks like crew rostering. By formulating Air France KLM’s rostering problem as a Quadratic Unconstrained Optimization (QUBO) problem, we found solutions by using quantum annealing, classical-quantum hybrid annealing and simulated annealing.

Simulated Annealing (SA) versus Hybrid Quantum solvers (HQPU). On the x-axis the number of days for which rosters were scheduled and on the y-axis the amount of constraints violated and the closeness of the found solution.

The Benefits

The fully quantum annealers already achieve close to the optimal schedule, while the hybrid solvers outperform both the quantum annealers and the simulated annealers. By utilizing quantum annealing, the solver could in future generate optimal rosters that conform to regulations, preferences, and operational needs, far more efficiently than traditional methods.

This work is supported by the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme

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Dutch DSO Alliander is faced with the challenge of increasing the capacity of their network within the next 10 years by the same amount as within the past 100 years. On top of that, novel technologies like solar panels and electric vehicles add additional complexities to this future network. Performing large grid calculations on this future network may become classically intractable.
Together, Alliander and QAL embarked on a journey to explore the potential usefulness of quantum computing for determining whether energy grids are robust enough to sustain potential cable outages. In the DSO community, this problem is referred to as the “N-1 problem”, and it comes down to being able to reroute the energy flow through a grid for every potential single-cable outage.

The Quantum Solution

During this initial collaboration, 3 potential quantum computing solutions were researched. Aimed at more fault-tolerant usages of quantum computing, the first method was based on amplitude amplification. By preparing a superposition over many different network configurations, we exploit quantum parallelism to efficiently find a valid network reconfiguration. In the second approach, we used quantum annealing, encoding our problem as a Quadratic Unconstrained Binary Optimization problem to let a quantum system adiabatically evolve towards our preferred solution. Lastly, we explored the use of Gaussian Boson Samplers for efficiently checking connectivity of networks after a cable outage disconnects them.

The Benefits

The amplitude amplification algorithm was tested on quantum emulators and was successfully run to solve the N-1 problem for graphs of up to size 7. Quantum annealing was run on D-Wave’s advantage system to solve the N-1 problem for graphs of size 4. The potential of photonic quantum computing was explored using QuiX Quantum’s Gaussian boson samplers.
These results indicate that as hardware quality and size advance, robustness of large systems that is classically incomputable, could potentially be verified on a quantum computer.

This work is supported by the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme

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“[…] I was personally astonished with the development and the maturity of the software ecosystem, where many libraries are already doing a lot of very exciting things.”

Nicolas Renaud

The collaboration between the eScience Centre, QAL and ASTRON on quantum computing for radio astronomy emerged naturally from the existing partnership between the Centre and Astron and in particular Dr. Chris Broekema.

Interpreting and processing radioastronomy data comprises a large and expansive computational pipeline, handling extraordinarily substantial amounts of data. Different sections of this pipeline could potentially benefit from offloading computations to a quantum processor. The main application explored was in image calibration.

In image calibration, we are tasked with reconstructing an image using data collected by multiple antennas. Due to atmospheric conditions or issues in the electronics connecting the antennas, this data needs to be recalibrated before the image can be reconstructed. The calibration requires solving large linear systems, a task at which quantum computers are known to excel. More on this work can be found in this recent publication on the results: link.

After the successful conclusion of this project, quantum computing application development for the eScience Centre and QAL continues. From streamlining the integration of quantum computing into classical quantum chemistry workflows to exploring new frontiers, the eScience Centre is poised to embrace together with QAL the exciting possibilities that lie ahead.

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Bathymetry is the study of water depths and at S[&]T this is done through the analysis of remote sensing data. This is relevant to the Dutch Ministry of Defense for collecting situational intelligence to determine potential landing sites for amphibious crafts. The depth of ocean floors between 0 and 20m is derived from large amounts of multispectral satellite data, using advanced machine learning algorithms. The data consists of 13 spectral bands with a temporal resolution of 5 days and spatial resolution between 10 and 60m, leading to an incredibly large amount of data, that becomes intractable for classical methods.

The Quantum Solution

Quantum neural networks have the potential to arrive at high accuracies using small amounts of data, as it has been shown that quantum machine learning algorithms can generalize well from few data1. The downside is the difficulty in loading large data sets onto a quantum processor. To take full advantage of quantum hardware, a classical dimensionality-reduction was used to reduce the high spectral dimensionality of the available data, after which the data was embedded in a variational quantum classifier to classify the data into depth intervals.

Classically predicted water-depths off the coast of Venice on the left, and water-depths predicted using a quantum simulator on the right.

The Benefits

The quantum algorithm was run on a 4-qubit simulator, tested on real multi-spectral data over a region near the Mediterranean Sea, with promising results.  As demonstrated in the figure below, the variational quantum classifier achieved high accuracies for the ocean depth. We managed to faithfully reproduce traditional (classical machine learning) results as a first step toward exploring the benefits of quantum. In the process of working out the use case, we gained additional insights into ways to improve the classical solution as well.

Links

Ref: [1] Generalization in quantum machine learning from few training data | Nature Communications

Link to the PENNYLANE blog and code : https://pennylane.ai/blog/2023/08/tno_quantum_variational_classifier_powering_ml_workflows_with_quantum/

This work is supported by the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme

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Modern large scale radio telescopes are made of multiple antennas whose signal needs to be combined to form a clear picture of the night sky. During this process, the antenna system needs to be calibrated to digitally remove noise source and imperfection in the telescope setup. Classical calibration techniques are powerful but computationally demanding.

The Quantum Solution

Together with Astron, we have implemented quantum linear solvers relying on two different backends namely IBM quantum and DWave. We have integrated these quantum solvers in radioastronomy pipeline developed  for the operation of the HERA telescope and benchmark their performance against classical linear solvers. We have demonstrated that the performance of these solvers, in particular the ones relying on quantum annealers can quickly provide a first approximation of the solution that further be refined using classical approaches. The solvers are freely available on the QAL github an can readily be reused for any application requiring the solution of linear solvers.

The Benefits

The application of quantum computing methods for solving linear system of equations has always a been a promising avenue for quantum computing. The integration of these solvers in complete processing pipelines shows the possibility to use these solvers and offer a path forward to integrate quantum computers in the design and operation of large scale data acquisition pipeline of radioastronomy.

Links

Link to the paper : https://arxiv.org/abs/2310.11932

Link to the code : https://github.com/QuantumRadioAstronomy/hera_cal_quantum

Link to the VQLS library : https://github.com/QuantumApplicationLab/vqls-prototype

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Toyota Motor Europe, in collaboration with QAL, is delving into the realm of photocatalysis for water
splitting, a pivotal process in the sustainable production of hydrogen. The accurate simulation of
photocatalytic reactions stands as a complex, resource-intensive endeavor that demands innovative
computational methodologies.

Schematic diagram illustrating the process of a prototypical photocatalytic water splitting reaction: a water molecule is adsorbed on the catalyst, enters a transition state, and subsequently the water molecule is split into two. This is the rate-determining step in this reaction.

The Quantum Solution

The project employs a state-averaged orbital optimized variational quantum eigensolver (SA-OO-VQE) to calculate the interaction energies of heterogeneous photocatalysis for water splitting in the ground as well as excited states. This advanced quantum algorithm allows for the precise and efficient modeling of complex photocatalytic processes, providing an unprecedented level of detail and insight into the interactions at play during photocatalysis.

The Benefits

Being able to simulate chemical processes, such as the splitting of water into hydrogen, promises to be one of the main future applications of quantum computing. The use of quantum computing facilitates description of both ground and excited electronic states in the same footing, an essential ingredient for modelling photocatalysis reactions. It not only enhances the accuracy of the calculations but also provides profound insights into the reaction mechanisms, thereby expediting the research and development process. Calculations were run on a quantum emulator and as the collaboration continues and hardware advances, we expect to be able to model larger and more-realistic systems.

Contacts

Toyota Motor Europe, sachin.kinge@toyota-europe.com

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