arXiv subjects

Jonas Nüßlein

Publications and source records attributed to Jonas Nüßlein.

At least 19 recordsLinked to original sources

arXiv2025

Demonstrating Quantum Scaling Advantage in Approximate Optimization for Energy Coalition Formation with 100+ Agents

The formation of energy communities is pivotal for advancing decentralized and sustainable energy management. Within this context, Coalition Structure Generation (CSG) emerges as a promising framework. The complexity of CSG grows rapidly with the number of agents, making classical solvers impractical for even moderate sizes. This suggests CSG as an ideal candidate for benchmarking quantum algorithms against classical ones. Facing ongoing challenges in attaining computational quantum advantage for exact optimization, we pivot our focus to benchmarking quantum and classical solvers for approximate optimization. Approximate optimization is particularly critical for industrial use cases requiring real-time optimization, where finding high-quality solutions quickly is often more valuable than achieving exact solutions more slowly. Our findings indicate that quantum annealing (QA) on DWave can achieve solutions of comparable quality to our best classical solver, but with more favorable runtime scaling, showcasing an advantage. This advantage is observed when compared to solvers, such as Tabu search, simulated annealing, and the state-of-the-art solver Gurobi, in finding approximate solutions for energy community formation involving over 100 agents. DWave also surpasses 1-round QAOA on IBM hardware. Our findings represent the largest benchmark of quantum approximate optimizations for a real-world dense model beyond the hardware's native topology, where D-Wave demonstrates a scaling advantage.

quant-ph↗

arXiv2025

Evaluating Variational Quantum Circuit Architectures for Distributed Quantum Computing

Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One approach to scale QPUs is to connect multiple machines through quantum and classical channels to form clusters or even quantum networks. Using this paradigm, several smaller QPUs can collectively execute circuits that each would not be able on its own. However, communication between QPUs is costly as it requires generating and maintaining entanglement, and hence it should be used wisely. In this paper, we evaluate the architectures, and in particular the entanglement patterns, of variational quantum circuits in a distributed quantum computing (DQC) setting. That is, using Qiskit, we simulate the execution of an eight qubit circuit using four QPUs each with two computational and two communication qubits where non-local CX-gates are performed using the remote-CX protocol. We compare the performance of various circuits on a binary classification task where training is executed under ideal and testing under noisy conditions. The study provides initial results on suitable VQC architectures for the DQC paradigm, and indicates that a standard VQC baseline is not always the best choice, and alternative architectures that use entanglement between QPUs sparingly deliver better results under noise.

quant-ph↗

arXiv2025

The Questionable Influence of Entanglement in Quantum Optimisation Algorithms

The performance of the Variational Quantum Eigensolver (VQE) is promising compared to other quantum algorithms, but also depends significantly on the appropriate design of the underlying quantum circuit. Recent research by Bowles, Ahmend \& Schuld, 2024 [1] raises questions about the effectiveness of entanglement in circuits for quantum machine learning algorithms. In our paper we want to address questions about the effectiveness of state preparation via Hadamard gates and entanglement via CNOT gates in the realm of quantum optimisation. We have constructed a total of eight different circuits, varying in implementation details, solving a total of 100 randomly generated MaxCut problems. Our results show no improvement with Hadamard gates applied at the beginning of the circuits. Furthermore, also entanglement shows no positive effect on the solution quality in our small scale experiments. In contrast, the investigated circuits that used entanglement generally showed lower, as well as deteriorating results when the number of circuit layers is increased. Based on our results, we hypothesise that entanglement can play a coordinating role, such that changes in individual parameters are distributed across multiple qubits in quantum circuits, but that this positive effect can quickly be overdosed and turned negative. The verification of this hypothesis represents a challenge for future research and can have a considerable influence on the development of new hybrid algorithms.

quant-ph↗

arXiv2025

Towards Scalable Lottery Ticket Networks using Genetic Algorithms

Building modern deep learning systems that are not just effective but also efficient requires rethinking established paradigms for model training and neural architecture design. Instead of adapting highly overparameterized networks and subsequently applying model compression techniques to reduce resource consumption, a new class of high-performing networks skips the need for expensive parameter updates, while requiring only a fraction of parameters, making them highly scalable. The Strong Lottery Ticket Hypothesis posits that within randomly initialized, sufficiently overparameterized neural networks, there exist subnetworks that can match the accuracy of the trained original model-without any training. This work explores the usage of genetic algorithms for identifying these strong lottery ticket subnetworks. We find that for instances of binary and multi-class classification tasks, our approach achieves better accuracies and sparsity levels than the current state-of-the-art without requiring any gradient information. In addition, we provide justification for the need for appropriate evaluation metrics when scaling to more complex network architectures and learning tasks.

cs.LG↗

arXiv2025

Grid Cost Allocation in Peer-to-Peer Electricity Markets: Benchmarking Classical and Quantum Optimization Approaches

This paper presents a novel optimization approach for allocating grid operation costs in Peer-to-Peer (P2P) electricity markets using Quantum Computing (QC). We develop a Quadratic Unconstrained Binary Optimization (QUBO) model that matches logical power flows between producer-consumer pairs with the physical power flow to distribute grid usage costs fairly. The model is evaluated on IEEE test cases with up to 57 nodes, comparing Quantum Annealing (QA), hybrid quantum-classical algorithms, and classical optimization approaches. Our results show that while the model effectively allocates grid operation costs, QA performs poorly in comparison despite extensive hyperparameter optimization. The classical branch-and-cut method outperforms all solvers, including classical heuristics, and shows the most advantageous scaling behavior. The findings may suggest that binary least-squares optimization problems may not be suitable candidates for near-term quantum utility.

quant-ph↗

arXiv2025

Multi-Agent Quantum Reinforcement Learning using Evolutionary Optimization

Multi-Agent Reinforcement Learning is becoming increasingly more important in times of autonomous driving and other smart industrial applications. Simultaneously a promising new approach to Reinforcement Learning arises using the inherent properties of quantum mechanics, reducing the trainable parameters of a model significantly. However, gradient-based Multi-Agent Quantum Reinforcement Learning methods often have to struggle with barren plateaus, holding them back from matching the performance of classical approaches. While gradient free Quantum Reinforcement Learning methods may alleviate some of these challenges, they too are not immune to the difficulties posed by barren plateaus. We build upon an existing approach for gradient free Quantum Reinforcement Learning and propose three genetic variations with Variational Quantum Circuits for Multi-Agent Reinforcement Learning using evolutionary optimization. We evaluate our genetic variations in the Coin Game environment and also compare them to classical approaches. We showed that our Variational Quantum Circuit approaches perform significantly better compared to a neural network with a similar amount of trainable parameters. Compared to the larger neural network, our approaches archive similar results using $97.88\%$ less parameters.

quant-ph↗

arXiv2024

Reducing QUBO Density by Factoring Out Semi-Symmetries

Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing are prominent approaches for solving combinatorial optimization problems, such as those formulated as Quadratic Unconstrained Binary Optimization (QUBO). These algorithms aim to minimize the objective function $x^T Q x$, where $Q$ is a QUBO matrix. However, the number of two-qubit CNOT gates in QAOA circuits and the complexity of problem embeddings in Quantum Annealing scale linearly with the number of non-zero couplings in $Q$, contributing to significant computational and error-related challenges. To address this, we introduce the concept of \textit{semi-symmetries} in QUBO matrices and propose an algorithm for identifying and factoring these symmetries into ancilla qubits. \textit{Semi-symmetries} frequently arise in optimization problems such as \textit{Maximum Clique}, \textit{Hamilton Cycles}, \textit{Graph Coloring}, and \textit{Graph Isomorphism}. We theoretically demonstrate that the modified QUBO matrix $Q_{\text{mod}}$ retains the same energy spectrum as the original $Q$. Experimental evaluations on the aforementioned problems show that our algorithm reduces the number of couplings and QAOA circuit depth by up to $45\%$. For Quantum Annealing, these reductions also lead to sparser problem embeddings, shorter qubit chains and better performance. This work highlights the utility of exploiting QUBO matrix structure to optimize quantum algorithms, advancing their scalability and practical applicability to real-world combinatorial problems.

quant-ph↗

arXiv2024

Swarm Behavior Cloning

In sequential decision-making environments, the primary approaches for training agents are Reinforcement Learning (RL) and Imitation Learning (IL). Unlike RL, which relies on modeling a reward function, IL leverages expert demonstrations, where an expert policy $π_e$ (e.g., a human) provides the desired behavior. Formally, a dataset $D$ of state-action pairs is provided: $D = {(s, a = π_e(s))}$. A common technique within IL is Behavior Cloning (BC), where a policy $π(s) = a$ is learned through supervised learning on $D$. Further improvements can be achieved by using an ensemble of $N$ individually trained BC policies, denoted as $E = {π_i(s)}{1 \leq i \leq N}$. The ensemble's action $a$ for a given state $s$ is the aggregated output of the $N$ actions: $a = \frac{1}{N} \sum{i} π_i(s)$. This paper addresses the issue of increasing action differences -- the observation that discrepancies between the $N$ predicted actions grow in states that are underrepresented in the training data. Large action differences can result in suboptimal aggregated actions. To address this, we propose a method that fosters greater alignment among the policies while preserving the diversity of their computations. This approach reduces action differences and ensures that the ensemble retains its inherent strengths, such as robustness and varied decision-making. We evaluate our approach across eight diverse environments, demonstrating a notable decrease in action differences and significant improvements in overall performance, as measured by mean episode returns.

cs.AI↗

arXiv2024

Optimizing Sensor Redundancy in Sequential Decision-Making Problems

Reinforcement Learning (RL) policies are designed to predict actions based on current observations to maximize cumulative future rewards. In real-world applications (i.e., non-simulated environments), sensors are essential for measuring the current state and providing the observations on which RL policies rely to make decisions. A significant challenge in deploying RL policies in real-world scenarios is handling sensor dropouts, which can result from hardware malfunctions, physical damage, or environmental factors like dust on a camera lens. A common strategy to mitigate this issue is the use of backup sensors, though this comes with added costs. This paper explores the optimization of backup sensor configurations to maximize expected returns while keeping costs below a specified threshold, C. Our approach uses a second-order approximation of expected returns and includes penalties for exceeding cost constraints. We then optimize this quadratic program using Tabu Search, a meta-heuristic algorithm. The approach is evaluated across eight OpenAI Gym environments and a custom Unity-based robotic environment (RobotArmGrasping). Empirical results demonstrate that our quadratic program effectively approximates real expected returns, facilitating the identification of optimal sensor configurations.

cs.RO↗

arXiv2024

Reducing QAOA Circuit Depth by Factoring out Semi-Symmetries

QAOA is a quantum algorithm for solving combinatorial optimization problems. It is capable of searching for the minimizing solution vector $x$ of a QUBO problem $x^TQx$. The number of two-qubit CNOT gates in the QAOA circuit scales linearly in the number of non-zero couplings of $Q$ and the depth of the circuit scales accordingly. Since CNOT operations have high error rates it is crucial to develop algorithms for reducing their number. We, therefore, present the concept of \textit{semi-symmetries} in QUBO matrices and an algorithm for identifying and factoring them out into ancilla qubits. \textit{Semi-symmetries} are prevalent in QUBO matrices of many well-known optimization problems like \textit{Maximum Clique}, \textit{Hamilton Cycles}, \textit{Graph Coloring}, \textit{Vertex Cover} and \textit{Graph Isomorphism}, among others. We theoretically show that our modified QUBO matrix $Q_{mod}$ describes the same energy spectrum as the original $Q$. Experiments conducted on the five optimization problems mentioned above demonstrate that our algorithm achieved reductions in the number of couplings by up to $49\%$ and in circuit depth by up to $41\%$.

quant-ph↗

arXiv2024

Evaluating Quantum Optimization for Dynamic Self-Reliant Community Detection

Power grid partitioning is an important requirement for resilient distribution grids. Since electricity production is progressively shifted to the distribution side, dynamic identification of self-reliant grid subsets becomes crucial for operation. This problem can be represented as a modification to the well-known NP-hard Community Detection (CD) problem. We formulate it as a Quadratic Unconstrained Binary Optimization (QUBO) problem suitable for solving using quantum computation{\color{blue}, which is expected to find better-quality partitions faster. The formulation aims to find communities with maximal self-sufficiency and minimal power flowing between them}. To assess quantum optimization for sizeable problems, we apply a hierarchical divisive method that solves sub-problem QUBOs to perform grid bisections. Furthermore, we propose a customization of the Louvain heuristic that includes self-reliance. In the evaluation, we first demonstrate that this problem examines exponential runtime scaling classically. Then, using different IEEE power system test cases, we benchmark the solution quality for multiple approaches: D-Wave's hybrid quantum-classical solvers, classical heuristics, and a branch-and-bound solver. As a result, we observe that the hybrid solvers provide very promising results, both with and without the divisive algorithm, regarding solution quality achieved within a given time frame. Directly utilizing D-Wave's Quantum Annealing (QA) hardware shows inferior partitioning.

quant-ph↗

arXiv2024

Solving Max-3SAT Using QUBO Approximation

As contemporary quantum computers do not possess error correction, any calculation performed by these devices can be considered an involuntary approximation. To solve a problem on a quantum annealer, it has to be expressed as an instance of Quadratic Unconstrained Binary Optimization (QUBO). In this work, we thus study whether systematically approximating QUBO representations of the MAX-3SAT problem can improve the solution quality when solved on contemporary quantum hardware, compared to using exact, non-approximated QUBO representations. For a MAX-3SAT instance consisting of a 3SAT formula with n variables and m clauses, we propose a method of systematically creating approximate QUBO representations of dimension (n x n), which is significantly smaller than the QUBO matrices of any exact, non-approximated MAX-3SAT QUBO transformation. In an empirical evaluation, we demonstrate that using our QUBO approximations for solving MAX-3SAT problems on D-Wave's quantum annealer Advantage_System6.4 can yield better results than using state-of-the-art exact QUBO transformations. Furthermore, we demonstrate that using naive QUBO approximation methods, based on removing values from exact (n+m)x(n+m)-dimensional QUBO representations of MAX-3SAT instances is ineffective.

quant-ph↗

arXiv2024

Towards Less Greedy Quantum Coalition Structure Generation in Induced Subgraph Games

The transition to 100% renewable energy requires new techniques for managing energy networks, such as dividing them into sensible subsets of prosumers called micro-grids. Doing so in an optimal manner is a difficult optimization problem, as it can be abstracted to the Coalition Structure Generation problem in Induced Subgraph Games, a NP-complete problem which requires dividing an undirected, complete, weighted graph into subgraphs in a way that maximizes the sum of their internal weights. Recently, Venkatesh et al. (arXiv:2212.11372) published a Quantum Annealing (QA)-based iterative algorithm called GCS-Q, which they claim to be the best currently existing solver for the problem in terms of runtime complexity. As this algorithm makes the application of QA to the problem seem promising, but is a greedy one, this work proposes several less greedy QA-based approaches and investigates whether any of them can outperform GCS-Q in terms of solution quality. While we find that this is not the case yet on D-Wave hardware, most of them do when using the classical QBSolv software as a solver. Especially an algorithm we call 4-split iterative R-QUBO shows potential here, finding all optima in our dataset while scaling favorably with the problem size in terms of runtime. Thus, it appears to be interesting for future research on quantum approaches to the problem, assuming QA hardware will become more noise-resilient over time.

quant-ph↗

arXiv2024

Architectural Influence on Variational Quantum Circuits in Multi-Agent Reinforcement Learning: Evolutionary Strategies for Optimization

In recent years, Multi-Agent Reinforcement Learning (MARL) has found application in numerous areas of science and industry, such as autonomous driving, telecommunications, and global health. Nevertheless, MARL suffers from, for instance, an exponential growth of dimensions. Inherent properties of quantum mechanics help to overcome these limitations, e.g., by significantly reducing the number of trainable parameters. Previous studies have developed an approach that uses gradient-free quantum Reinforcement Learning and evolutionary optimization for variational quantum circuits (VQCs) to reduce the trainable parameters and avoid barren plateaus as well as vanishing gradients. This leads to a significantly better performance of VQCs compared to classical neural networks with a similar number of trainable parameters and a reduction in the number of parameters by more than 97 \% compared to similarly good neural networks. We extend an approach of Kölle et al. by proposing a Gate-Based, a Layer-Based, and a Prototype-Based concept to mutate and recombine VQCs. Our results show the best performance for mutation-only strategies and the Gate-Based approach. In particular, we observe a significantly better score, higher total and own collected coins, as well as a superior own coin rate for the best agent when evaluated in the Coin Game environment.

quant-ph↗

arXiv2024

Incentivising Demand Side Response through Discount Scheduling using Hybrid Quantum Optimization

Demand Side Response (DSR) is a strategy that enables consumers to actively participate in managing electricity demand. It aims to alleviate strain on the grid during high demand and promote a more balanced and efficient use of (renewable) electricity resources. We implement DSR through discount scheduling, which involves offering discrete price incentives to consumers to adjust their electricity consumption patterns to times when their local energy mix consists of more renewable energy. Since we tailor the discounts to individual customers' consumption, the Discount Scheduling Problem (DSP) becomes a large combinatorial optimization task. Consequently, we adopt a hybrid quantum computing approach, using D-Wave's Leap Hybrid Cloud. We benchmark Leap against Gurobi, a classical Mixed Integer optimizer in terms of solution quality at fixed runtime and fairness in terms of discount allocation. Furthermore, we propose a large-scale decomposition algorithm/heuristic for the DSP, applied with either quantum or classical computers running the subroutines, which significantly reduces the problem size while maintaining solution quality. Using synthetic data generated from real-world data, we observe that the classical decomposition method obtains the best overall \newp{solution quality for problem sizes up to 3200 consumers, however, the hybrid quantum approach provides more evenly distributed discounts across consumers.

quant-ph↗

arXiv2024

Enhancing Quantum Algorithms for Quadratic Unconstrained Binary Optimization via Integer Programming

To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer programming. State-of-the-art integer programming algorithms can compute strong relaxation bounds even for hard instances, but may have to enumerate a large number of subproblems for determining an optimum solution. If the potential of quantum computing realizes, it can be expected that in particular finding high-quality solutions for hard problems can be done fast. Still, near-future quantum hardware considerably limits the size of treatable problems. In this work, we go one step into integrating the potentials of quantum and classical techniques for combinatorial optimization. We propose a hybrid heuristic for the weighted maximum-cut problem or, equivalently, for quadratic unconstrained binary optimization. The heuristic employs a linear programming relaxation, rendering it well-suited for integration into exact branch-and-cut algorithms. For large instances, we reduce the problem size according to a linear relaxation such that the reduced problem can be handled by quantum machines of limited size. Moreover, we improve the applicability of QAOA, a parameterized quantum algorithm, by deriving optimal parameters for special instances which motivates a parameter estimate for arbitrary instances. We present numerous computational results from real quantum hardware.

quant-ph↗

arXiv2024

Qandle: Accelerating State Vector Simulation Using Gate-Matrix Caching and Circuit Splitting

To address the computational complexity associated with state-vector simulation for quantum circuits, we propose a combination of advanced techniques to accelerate circuit execution. Quantum gate matrix caching reduces the overhead of repeated applications of the Kronecker product when applying a gate matrix to the state vector by storing decomposed partial matrices for each gate. Circuit splitting divides the circuit into sub-circuits with fewer gates by constructing a dependency graph, enabling parallel or sequential execution on disjoint subsets of the state vector. These techniques are implemented using the PyTorch machine learning framework. We demonstrate the performance of our approach by comparing it to other PyTorch-compatible quantum state-vector simulators. Our implementation, named Qandle, is designed to seamlessly integrate with existing machine learning workflows, providing a user-friendly API and compatibility with the OpenQASM format. Qandle is an open-source project hosted on GitHub https://github.com/gstenzel/qandle and PyPI https://pypi.org/project/qandle/ .

quant-ph↗

arXiv2024

Quantum Optimization for the Future Energy Grid: Summary and Quantum Utility Prospects

In this project summary paper, we summarize the key results and use-cases explored in the German Federal Ministry of Education and Research (BMBF) funded project "Q-GRID" which aims to assess potential quantum utility optimization applications in the electrical grid. The project focuses on two layers of optimization problems relevant to decentralized energy generation and transmission as well as novel energy transportation/exchange methods such as Peer-2-Peer energy trading and microgrid formation. For select energy grid optimization problems, we demonstrate exponential classical optimizer runtime scaling even for small problem instances, and present initial findings that variational quantum algorithms such as QAOA and hybrid quantum annealing solvers may provide more favourable runtime scaling to obtain similar solution quality. These initial results suggest that quantum computing may be a key enabling technology in the future energy transition insofar that they may be able to solve business problems which are already challenging at small problem instance sizes.

quant-ph↗