arXiv subjects

Claudia Linnhoff-Popien

Publications and source records attributed to Claudia Linnhoff-Popien.

At least 55 records · Page 3Linked to original sources

arXiv2025

Investigating Parameter-Efficiency of Hybrid QuGANs Based on Geometric Properties of Generated Sea Route Graphs

The demand for artificially generated data for the development, training and testing of new algorithms is omnipresent. Quantum computing (QC), does offer the hope that its inherent probabilistic functionality can be utilised in this field of generative artificial intelligence. In this study, we use quantum-classical hybrid generative adversarial networks (QuGANs) to artificially generate graphs of shipping routes. We create a training dataset based on real shipping data and investigate to what extent QuGANs are able to learn and reproduce inherent distributions and geometric features of this data. We compare hybrid QuGANs with classical Generative Adversarial Networks (GANs), with a special focus on their parameter efficiency. Our results indicate that QuGANs are indeed able to quickly learn and represent underlying geometric properties and distributions, although they seem to have difficulties in introducing variance into the sampled data. Compared to classical GANs of greater size, measured in the number of parameters used, some QuGANs show similar result quality. Our reference to concrete use cases, such as the generation of shipping data, provides an illustrative example and demonstrate the potential and diversity in which QC can be used.

cs.LG↗

arXiv2025

Quantum Boltzmann Machines using Parallel Annealing for Medical Image Classification

Exploiting the fact that samples drawn from a quantum annealer inherently follow a Boltzmann-like distribution, annealing-based Quantum Boltzmann Machines (QBMs) have gained increasing popularity in the quantum research community. While they harbor great promises for quantum speed-up, their usage currently stays a costly endeavor, as large amounts of QPU time are required to train them. This limits their applicability in the NISQ era. Following the idea of Noè et al. (2024), who tried to alleviate this cost by incorporating parallel quantum annealing into their unsupervised training of QBMs, this paper presents an improved version of parallel quantum annealing that we employ to train QBMs in a supervised setting. Saving qubits to encode the inputs, the latter setting allows us to test our approach on medical images from the MedMNIST data set (Yang et al., 2023), thereby moving closer to real-world applicability of the technology. Our experiments show that QBMs using our approach already achieve reasonable results, comparable to those of similarly-sized Convolutional Neural Networks (CNNs), with markedly smaller numbers of epochs than these classical models. Our parallel annealing technique leads to a speed-up of almost 70 % compared to regular annealing-based BM executions.

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arXiv2025

Efficient QAOA Architecture for Solving Multi-Constrained Optimization Problems

This paper proposes a novel combination of constraint encoding methods for the Quantum Approximate Optimization Ansatz (QAOA). Real-world optimization problems typically consist of multiple types of constraints. To solve these optimization problems with quantum methods, normally, all constraints are added as quadratic penalty terms to the objective, which expands the search space and increases problem complexity. This work proposes a general workflow that extracts and encodes specific constraints directly into the circuit of QAOA: One-hot constraints are enforced through $XY$-mixers that restrict the search space to the feasible sub-space naturally. Inequality constraints are implemented through oracle-based Indicator Functions (IF). This paper focuses on the numerical benchmarks of the combined approach for solving the Multi-Knapsack (MKS) and the Prosumer Problem (PP), a modification of the MKS in the domain of electricity optimization. To this end, we introduce computational techniques that efficiently simulate the two presented constraint architectures. Since $XY$-mixers restrict the search space, specific state vector entries are always zero and can be omitted from the simulation, saving valuable memory and computing resources. We benchmark the combined method against the established QUBO formulation, yielding a better solution quality and probability of sampling the optimal solution. Despite more complex circuits, the time-to-solution is more than an order of magnitude faster compared to the baseline methods and exhibits more favorable scaling properties.

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arXiv2025

Time-Aware Qubit Assignment and Circuit Optimization for Distributed Quantum Computing

The emerging paradigm of distributed quantum computing promises a potential solution to scaling quantum computing to currently unfeasible dimensions. While this approach itself is still in its infancy, and many obstacles must still be overcome before its physical implementation, challenges from the software and algorithmic side must also be identified and addressed. For instance, this paradigm shift requires a new form of compiler that considers the network constraints in general as well as phenomena arising due to the nature of quantum communication. In distributed quantum computing, large circuits are divided into smaller subcircuits such that they can be executed individually and simultaneously on multiple QPUs that are connected through quantum channels. As quantum communication, for example, in the form of teleportation, is expensive, it must be used sparingly. We address the problem of assigning qubits to QPUs to minimize communication costs in two different ways. First by applying time-aware algorithms that take into account the changing connectivity of a given circuit as well as the underlying network topology. We define the optimization problem, use simulated annealing and an evolutionary algorithm and compare the results to graph partitioning and sequential qubit assignment baselines. In another approach, we propose an evolutionary-based quantum circuit optimization algorithm that adjusts the circuit itself rather than the schedule to reduce the overall communication cost. We evaluate the techniques against random circuits and different network topologies. Both evolutionary algorithms outperform the baseline in terms of communication cost reduction. We give an outlook on how the approaches can be integrated into a compilation framework for distributed quantum computing.

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arXiv2025

Clique detection using symmetry-restricted quantum circuits

We show the application of permutation-invariant quantum circuits to the clique problem. The experiment asks to label a clique through identification of the nodes in a larger subgraph. The permutation-invariant quantum circuit outperforms a cyclic-invariant alternative as well as a standard quantum machine learning ansatz. We explain the behavior through the intrinsic symmetry of the problem, in the sense that the problem is symmetric under permutation of both the feature and the label.

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arXiv2025

Analysis of quantum neural network performance via edge cases

We evaluate the particular performance of different quantum machine learning networks on a graph classification task. Quantum circuits with varying internal symmetry that completely, partially and not at all confer to the symmetry of the graph show different performance on the data set. The convergence results are inspected using a number of special graphs with particular structure. These are unlikely to occur in the training data and cover specific cases that refute the assumption that the quantum neural network learns simpler surrogate models based on the number of edges in the graph.

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arXiv2025

Scaling of symmetry-restricted quantum circuits

The intrinsic symmetries of physical systems have been employed to reduce the number of degrees of freedom of systems, thereby simplifying computations. In this work, we investigate the properties of $\mathcal{M}SU(2^N)$, $\mathcal{M}$-invariant subspaces of the special unitary Lie group $SU(2^N)$ acting on $N$ qubits, for some $\mathcal{M}\subseteq M_{2^N}(\mathbb{C})$. We demonstrate that for certain choices of $\mathcal{M}$, the subset $\mathcal{M}SU(2^N)$ inherits many topological and group properties from $SU(2^N)$. We then present a combinatorial method for computing the dimension of such subspaces when $\mathcal{M}$ is a representation of a permutation group acting on qubits $(GSU(2^N))$, or a Hamiltonian $(H^{(N)}SU(2^N))$. The Kronecker product of $\mathfrak{su}(2)$ matrices is employed to construct the Lie algebras associated with different permutation-invariant groups $GSU(2^N)$. Numerical results on the number of dimensions support the the developed theory.

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arXiv2025

Solving graph problems using permutation-invariant quantum machine learning

Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond to the specific symmetry of the problem. We investigate this adaption of the quantum circuit to the problem symmetry on graph classification problems. On random graphs, the quantum machine learning ansatz classifies whether a given random graph is connected, bipartite, contains a Hamiltonian path or cycle, respectively. We find that if the quantum circuit reflects the inherent symmetry of the problem, it vastly outperforms the standard, unsymmetrized ansatzes. Even when the symmetry is only approximative, there is still a significant performance gain over non-symmetrized ansatzes. We show how the symmetry can be included in the quantum circuit in a straightforward constructive method.

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arXiv2025

Quantum Circuit Construction and Optimization through Hybrid Evolutionary Algorithms

We apply a hybrid evolutionary algorithm to minimize the depth of circuits in quantum computing. More specifically, we evaluate two different variants of the algorithm. In the first approach, we combine the evolutionary algorithm with an optimization subroutine to optimize the parameters of the rotation gates present in the quantum circuit. In the second, the algorithm solely relies on evolutionary operations (i.e., mutations and crossover). We approach the problem from two sides: (1) constructing circuits from the ground up by starting with random initializations and (2) initializing individuals with a target circuit in order to optimize it further according to the fitness function. We run experiments on random circuits with 4 and 6 qubits varying in circuit depth. Our results show that the proposed methods are able to significantly reduce the depth of circuits while still retaining a high fidelity to the target state.

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arXiv2025

Surrogate Fitness Metrics for Interpretable Reinforcement Learning

We employ an evolutionary optimization framework that perturbs initial states to generate informative and diverse policy demonstrations. A joint surrogate fitness function guides the optimization by combining local diversity, behavioral certainty, and global population diversity. To assess demonstration quality, we apply a set of evaluation metrics, including the reward-based optimality gap, fidelity interquartile means (IQMs), fitness composition analysis, and trajectory visualizations. Hyperparameter sensitivity is also examined to better understand the dynamics of trajectory optimization. Our findings demonstrate that optimizing trajectory selection via surrogate fitness metrics significantly improves interpretability of RL policies in both discrete and continuous environments. In gridworld domains, evaluations reveal significantly enhanced demonstration fidelities compared to random and ablated baselines. In continuous control, the proposed framework offers valuable insights, particularly for early-stage policies, while fidelity-based optimization proves more effective for mature policies. By refining and systematically analyzing surrogate fitness functions, this study advances the interpretability of RL models. The proposed improvements provide deeper insights into RL decision-making, benefiting applications in safety-critical and explainability-focused domains.

cs.LG↗

arXiv2025

Quality Diversity for Variational Quantum Circuit Optimization

Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned VQC optimization, but are either slow, sample inefficient or require infeasible circuit depth to realize advantages. Quality diversity (QD) search methods combine diversity-driven optimization with user-specified features that offer insight into the optimization quality of circuit solution candidates. However, the choice of quality measures and the representational modeling of the circuits to allow for optimization with the current state-of-the-art QD methods like covariance matrix adaptation (CMA), is currently still an open problem. In this work we introduce a directly matrix-based circuit engineering, that can be readily optimized with QD-CMA methods and evaluate heuristic circuit quality properties like expressivity and gate-diversity as quality measures. We empirically show superior circuit optimization of our QD optimization w.r.t. speed and solution score against a set of robust benchmark algorithms from the literature on a selection of NP-hard combinatorial optimization problems.

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arXiv2025

IF-QAOA: A Penalty-Free Approach to Accelerating Constrained Quantum Optimization

Traditional methods for handling (inequality) constraints in the Quantum Approximate Optimization Ansatz (QAOA) typically rely on penalty terms and slack variables, which increase problem complexity and expand the search space. More sophisticated mixer-based QAOA variants restrict the search within the feasible assignments but often suffer from prohibitive circuit complexity. This paper presents a low-complexity formalism for incorporating inequality constraints into the cost function of QAOA using an oracle-based subroutine that evaluates constraint satisfaction in an additional register, subsequently called Indicator Function QAOA (IF-QAOA). The IF-QAOA cost function consists of a step-function but does not require a penalty term with additional parameters. Applied to the Knapsack problem, we demonstrate the superior performance of IF-QAOA over conventional penalty-based approaches in simulated experiments. Using advanced QAOA simulation techniques with instances consisting of up to 22 items, we find that IF-QAOA achieves significantly higher solution quality and a faster time-to-solution in 82% of our benchmark cases. Analysis of the scaling behavior shows favorable scaling of IF-QAOA compared to penalty-based methods. Also, benchmarked against the recently developed Quantum Tree Generator QAOA for Knapsack Problems, we demonstrate higher solution quality for circuits of similar complexity. Additionally, the paper introduces a method for approximate indicator function when the number of ancillary qubits is limited. With a specialized simulation algorithm based on projective measurements, we empirically demonstrate that a fixed number of ancillary qubits is sufficient to encode general inequality constraints.

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arXiv2025

Evaluating Parameter-Based Training Performance of Neural Networks and Variational Quantum Circuits

In recent years, neural networks (NNs) have driven significant advances in machine learning. However, as tasks grow more complex, NNs often require large numbers of trainable parameters, which increases computational and energy demands. Variational quantum circuits (VQCs) offer a promising alternative: they leverage quantum mechanics to capture intricate relationships and typically need fewer parameters. In this work, we evaluate NNs and VQCs on simple supervised and reinforcement learning tasks, examining models with different parameter sizes. We simulate VQCs and execute selected parts of the training process on real quantum hardware to approximate actual training times. Our results show that VQCs can match NNs in performance while using significantly fewer parameters, despite longer training durations. As quantum technology and algorithms advance, and VQC architectures improve, we posit that VQCs could become advantageous for certain machine learning tasks.

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arXiv2025

Evaluating Mutation Techniques in Genetic Algorithm-Based Quantum Circuit Synthesis

Quantum computing leverages the unique properties of qubits and quantum parallelism to solve problems intractable for classical systems, offering unparalleled computational potential. However, the optimization of quantum circuits remains critical, especially for noisy intermediate-scale quantum (NISQ) devices with limited qubits and high error rates. Genetic algorithms (GAs) provide a promising approach for efficient quantum circuit synthesis by automating optimization tasks. This work examines the impact of various mutation strategies within a GA framework for quantum circuit synthesis. By analyzing how different mutations transform circuits, it identifies strategies that enhance efficiency and performance. Experiments utilized a fitness function emphasizing fidelity, while accounting for circuit depth and T operations, to optimize circuits with four to six qubits. Comprehensive hyperparameter testing revealed that combining delete and swap strategies outperformed other approaches, demonstrating their effectiveness in developing robust GA-based quantum circuit optimizers.

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arXiv2025

Accelerated VQE: Parameter Recycling for Similar Recurring Problem Instances

Training the Variational Quantum Eigensolver (VQE) is a task that requires substantial compute. We propose the use of concepts from transfer learning to considerably reduce the training time when solving similar problem instances. We demonstrate that its utilisation leads to accelerated convergence and provides a similar quality of results compared to circuits with parameters initialised around zero. Further, transfer learning works better when the distance between the source-solution is close to that of the target-solution. Based on these findings, we present an accelerated VQE approach tested on the MaxCut problem with a problem size of 12 nodes solved with two different circuits utilised. We compare our results against a random baseline and non transfer learning trained circuits. Our experiments demonstrate that transfer learning can reduce training time by around 93\% in post-training, relative to identical circuits without the use of transfer learning. The accelerated VQE approach beats the standard approach by seven, respectively nine percentage points in terms of solution quality, if the early-stopping is considered. In settings where time-to-solution or computational costs are critical, this approach provides a significant advantage, having an improved trade-off between training effort and solution quality.

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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.

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arXiv2025

PIMAEX: Multi-Agent Exploration through Peer Incentivization

While exploration in single-agent reinforcement learning has been studied extensively in recent years, considerably less work has focused on its counterpart in multi-agent reinforcement learning. To address this issue, this work proposes a peer-incentivized reward function inspired by previous research on intrinsic curiosity and influence-based rewards. The \textit{PIMAEX} reward, short for Peer-Incentivized Multi-Agent Exploration, aims to improve exploration in the multi-agent setting by encouraging agents to exert influence over each other to increase the likelihood of encountering novel states. We evaluate the \textit{PIMAEX} reward in conjunction with \textit{PIMAEX-Communication}, a multi-agent training algorithm that employs a communication channel for agents to influence one another. The evaluation is conducted in the \textit{Consume/Explore} environment, a partially observable environment with deceptive rewards, specifically designed to challenge the exploration vs.\ exploitation dilemma and the credit-assignment problem. The results empirically demonstrate that agents using the \textit{PIMAEX} reward with \textit{PIMAEX-Communication} outperform those that do not.

cs.MA↗

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.

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