Student-Abstracts-EN

Using Evolutionary Algorithms for Quantum Circuit Optimization under Noise

Abstract:

Noise poses a prevalent challenge in the NISQ era of quantum computing. Its strong impact on the hardware of a quantum computer distorts the results of quantum circuits, especially with an increasing number of qubits and circuit depths. However, different circuit architectures that produce similar states can be exposed varying degrees of noise. This work presents an evolutionary algorithm aimed at finding an equivalent and less noisy circuit for a given quantum circuit. The algorithm’s fitness function evaluates the circuits based on their fidelity under noise compared to the noise-free state of the target circuit. With that, the evolutionary process is directed towards a noise-reduced solution. The results of the experiments show that the algorithm generally outperformed the randomly generated baseline and, in some cases, was able to find an optimized circuit compared to the target circuit. This demonstrates the potential of evolutionary algorithms for noise reduction. However, the scalability of the proposed evolutionary algorithm is severely limited.

Author:

Maria Trainer

Advisors:

Leo Sünkel, Maximilian Zorn, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published May 2025 | Copyright © QAR-Lab
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Analyzing the Parameter Adaption of Transfer Learning in Variational Quantum Eigensolvers

Abstract:

With the introduction of publicly available, yet noisy, Quantum Processors, many machine learning (ML) approaches have been proposed to make the most of the new capabilities. Peruzzo et al. proposed a hybrid algorithm, which implements a variational quantum eigensolver (VQE) to find the ground state of a Hamiltonian. While initially used in the field of quantum chemistry, VQEs can be used to solve a variety of optimization problems, such as finding a max-cut in a graph. As training is computationally expensive, transfer learning approaches have been proposed to reduce training time for similar problem instances. Rohe et al. introduce a VQE algorithm utilizing TL to speed up convergence in the max-cut problem. It was shown that TL is able to achieve convergence significantly faster in the early optimization phase, although training without TL yields slightly better results over time. However, when training time is drastically reduced, TL is able to produce good results while drastically reducing the computational cost of training. Furthermore, it was shown that the similarity of the optimal solution correlated positively with the success of TL. The similarity was measured by calculating the minimal hamming distance (HD) between the VQE’s solution of the source graph and the optimal solutions of the target graph. This thesis will be based primarily on the work done by Rohe et al. Specifically, the aim of the thesis is to analyze the quality of the parameter transfer to solve max-cut graph problems. Thus, instead of trying to demonstrate the applicability of TL for the VQE, it will be investigated where TL causes the algorithm to over- or under-adapt and how these results come about. The source-and target-graphs are sampled form the publicly available California street network as well as Facebook social circle data. Here the source graph will be utilized to train parameters which are to be transferred to initialize the training of the target graph. To evaluate the similarity of the source- and target-graph applied to the max-cut problem, the optimal max-cut solutions are calculated via brute force. Afterward the minimal HD between optimal solutions of the source and target-graphs are calculated. As TL might not always find one of the optimal solutions, the HD between the source solution and the target solution found through TL are calculated. This will provide information about whether TL caused the VQE to over- or under-adapt. As the quality of trained solutions appears to deteriorate as the HD between source- and target-graph solutions increase, it is of high interest to find ways to handle these kinds of problems. A possible explanation for over- or under-adaption is that the pre-trained parameters trap the VQE in a local optimum, inhibiting further exploration of the solution landscape. Through the analysis of the influence TL has on the training process of the VQE as well as under- and over-adaption, this thesis aims to better evaluate the role and quality of parameter transfer in the NISQ era.

Author:

Julio Amaru Nicolas Brocca Alvarado

Advisors:

Tobias Rohe, Sebastian Woelkert, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published April 2025 | Copyright © QAR-Lab
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Exploring Entanglement-intensity in Variational Quantum Eigensolver Algorithms for Combinatorial Optimization

Abstract:

Variational Quantum Algorithms (VQAs), including the Quantum Approximate Optimization Algorithm (QAOA), the Variational Quantum Eigensolver (VQE), and Quantum Neural Networks (QNNs), have emerged as promising approaches in the noisy intermediate-scale quantum (NISQ) era. These hybrid quantum-classical algorithms aim to solve optimization and simulation problems under the constraints of limited qubit connectivity, gate errors, and decoherence. A central feature of quantum computing, and a distinguishing factor from classical methods, is entanglement—the quantum correlation between qubits that enables certain computational advantages. While entanglement is widely considered essential for the success of VQAs, recent studies have challenged the assumption that more entanglement always improves algorithmic performance. Instead, excessive entanglement can introduce barren plateaus, increase optimization difficulty, and degrade convergence.
This work investigates the role of entanglement in the performance of the VQE, a leading algorithm for approximating ground-state energies of quantum Hamiltonians. Specifically, it explores whether limiting entanglement through structured reductions improves trainability and solution quality. To systematically analyze this relationship, two entanglement manipulation strategies are employed: (1) Dropout-based entanglement sparsification, where entangling gates are randomly removed based on a given probability, and (2) Parameterized entanglement tuning, where the strength of controlled entangling operations is constrained by a variable rotation parameter. The impact of these strategies is evaluated across three circuit ansätze by evaluating convergence behaviour as well as measuring three key-metrics: entangling capability, expressibility and approximation ratio. The results reveal that reducing entanglement via dropout improves optimization dynamics by potentially mitigating barren plateaus and increasing gradient variance, leading to faster convergence and lower final energies without compromising solution quality. However, the varying responses across different ansätze suggest that entanglement reduction should be tailored to circuit topology and problem structure rather than applied uniformly. In contrast, parameterized entanglement tuning shows a weaker influence on both trainability and final solution quality, particularly in deeper circuits where cumulative entanglement compensates for local gate-level adjustments. Notably, the study finds that convergence behavior serves as a more reliable indicator of VQE performance than expressibility or entangling capability alone, emphasizing that entanglement should be actively managed rather than maximized indiscriminately.

Autor/in:

Joel Friedrich

Betreuer:

Studentische Abschlussarbeit | Veröffentlicht April 2025 | Copyright © QAR-Lab
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Problem-Specific Entanglement in Variational Quantum Circuits

Abstract:

Over the last ten years, Variational Quantum Algorithms (VQAs), particularly the Variational Quantum Eigensolver (VQE), have emerged as promising approaches for approximately solving optimisation problems on the currently available Noisy Intermediate-Scale Quantum (NISQ) devices, which are prone to errors and quantum noise. In the VQE optimisation loop, a trial quantum state is prepared through a parametrised quantum circuit. A classical optimiser adjusts the circuit’s parameters, while the problem’s cost function is formulated into an Ising Hamiltonian. The cost function landscape’s global minimum is approximated through the iterative parametrised preparation of a trial quantum state, followed by the subsequent measuring of this state and the classical optimisation of parameters. Previous research showed the major influence, that the architecture of the parametrised circuit, so called ansatz, has on VQE’s optimisation performance.

Even though entanglement is a key property of quantum mechanics, it’s not well understood, if it can play a coordinating role in the ansatz circuit of hybrid quantum optimisation algorithms. While previous research showed that entanglement does not provide general benefits to optimisation when implemented in a generic, problem-agnostic way, this thesis investigates the role of problem-specific entanglement in variational quantum circuits, focusing on the Max-Cut problem, which is widely used in this field for benchmarking purposes and has practical applications in fields like very-large-scale-integrated (VLSI) circuit design, social networks and machine learning. The goal is to assess whether problem-specific entanglement structures can outperform problem-agnostic ones. In order to answer this question, we systematically compare different circuit architectures, including problem-specific, generic and randomised entanglement strategies, to analyse their impact on optimisation performance. For the problem-specific circuit design, we map the edges of the underlying Max-Cut graph as two-qubit gates onto the quantum circuit. Our results show that while our problem-specific entanglement approach converges slower across three considered problem sizes, it also consistently achieves similar approximated cost function minima compared to the generic design and shows significantly faster optimisation speeds than the randomised designs. Future work may explore this effect with larger problem sizes. Additionally, experiments in a simulated noisy environment show that quantum noise can accelerate early-stage convergence, possibly due to stochastic perturbations helping the optimizer escape local minima. This effect does not continue and ultimately decrease optimisation in the later phases. Furthermore we noticed, that increasing the amount of entanglement layers leads to diminishing
returns, likely due to over-parametrisation and reduced trainability.

Author:

Benjamin Nicolas Joseph Ring

Advisors:

Tobias Rohe, Julian Hager, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published April 2025 | Copyright © QAR-Lab
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Space-Efficient Quantum Optimization for the Traveling Salesman Problem via Binary Encoding of Feasible Solutions

Abstract:

The Traveling Salesperson Problem (TSP) is a classic combinatorial optimization problem with multiple applications in logistics, planning, and scheduling. Quantum algorithms, particularly the Quantum Approximate Optimization Algorithm (QAOA), have demonstrated potential for addressing such NP-hard problems and potentially can offer advantages over classical methods. Existing quantum approaches to the TSP typically rely on one-hot encoded states, requiring O(n^2) qubits for a TSP instance with n cities and using constraint-preserving mixers like the XY-mixer to navigate the feasible subspace. However, these methods are resource-intensive and face scalability issues due to the large number of qubits needed. This master thesis investigates a novel, space-efficient encoding scheme for solving the TSP using QAOA with a binary encoding of permutations, reducing the qubit requirement to O(n log2 n). The main challenge of binary encoding is the absence of an simple constraint-preserving mixer to maintain feasibility during optimization. To address this, an efficiently implementable unitary transformation was proposed to assign each binary-encoded tour a unique label. By adding O(log2 n!) ancillary qubits that represent each possible permutation of the TSP in factorial-base system, a canonical isomorphism between permutations and factorial-base numbers is established. The mixing operation is then performed on this ancillary space through a simpler X-mixer or a Grover mixer, automatically restricting the algorithm’s evolution to valid tours. This ensures that hard constraints remain satisfied throughout the optimization process, enabling faster convergence toward the optimal solution. Three variants of this encoding are explored in this master thesis: (1) a direct unitary transformation using a precomputed look-up table, (2) a quantum arithmetic–based method, and (3) an index-only approach that encodes both cost and mixer Hamiltonians in [log2(n!)] qubits, potentially introducing higher-order interactions. Numerical experiments with small problem instances demonstrate the feasibility of these approaches, highlighting the prospective benefits of this space-efficient encoding scheme in practical quantum optimization tasks.

Author:

Viktoria Patapovich

Advisors:

Jonas Stein, David Bucher, Claudia Linnhoff-Popien

Student Thesis | Published January 2025 | Copyright © QAR-Lab
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