arXiv subjects

Tobias Stollenwerk

Publications and source records attributed to Tobias Stollenwerk.

At least 19 recordsLinked to original sources

arXiv2026

Quantum search algorithm for similar subgraph identification under fixed edge removal

We introduce a novel quantum algorithm for similar subgraph identification in form of an NP-hard cardinality-constrained binary quadratic optimization problem. Given a weighted reference graph with Laplacian $\boldsymbol{B}$, our algorithm determines the subgraph featuring Laplacian $\boldsymbol{B'}$ on the same vertex set, but $x$ out of $N$ inactive edges, minimizing the Frobenius distance $||\boldsymbol{B} - \boldsymbol{B'}||_\mathrm{F}^2$. We represent the $\binom{N}{x}$ graph topologies by an equal-weight superposition in form of a Dicke state, enabling controlled transformations applied to the quantum state associated with the vectorized Laplacian of the reference graph. Combined with amplitude estimation and a minimum finding approach, our algorithm provides a polynomial speed up $\mathcal{O}(\sqrt{N^{x}/x!}N\log\log N)$ compared to $\mathcal{O}(N^{x+1}/x!)$ of classical brute-force search algorithms. We demonstrate the application of our method on standard test cases, which represent electric power grids, by reconstructing $||\boldsymbol{B} -\boldsymbol{B'}||_\mathrm{F}^2$ from measurements and show how our approach can be additionally used to calculate energy functional like quadratic forms of the Laplacians with respect to a given vector.

quant-ph↗

arXiv2025

Measurement-driven Quantum Approximate Optimization

Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak measurements related to imaginary-time evolution. In this work we specialize and extend this approach to the setting of combinatorial optimization. We first generalize the algorithm from exact to approximate optimization, taking advantage of several properties unique to classical problems. In particular we show how to select parameters such that the success probability of each measurement step is bounded away from $1/2$. We then show how to adapt our paradigm to the setting of constrained optimization for a number of important classes of hard problem constraints. For this we compare and contrast both penalty-based and feasibility-preserving approaches, elucidating the significant advantages of the latter approach. Our approach is general and may be applied to easy-to-prepare initial states as a standalone algorithm, or deployed as a quantum postprocessing stage to improve performance of a given parameterized quantum circuit. We then propose a more sophisticated variant of our algorithm that adaptively applies a mixing operator or not, based on the measurement outcomes seen so far, as to speeds up the algorithm and helps the system evolution avoid slowing down or getting stuck suboptimally. In particular, we show that mixing operators from the quantum alternating operator ansatz can be imported directly, both for the necessary eigenstate scrambling operator and for initial state preparation, and discuss quantum resource tradeoffs.

quant-ph↗

arXiv2025

Warm Start of Variational Quantum Algorithms for Quadratic Unconstrained Binary Optimization Problems

Variational Quantum Eigensolver (VQE) is widely used in near-term hardware. However, their performances remain limited by the poor trainability and are dependent on random parameter initialization. In this work, we propose a warm start method inspired by imaginary time evolution, allowing for determining initial parameters that prioritize lower energy states in a resource-efficient way. Using classical simulations, we demonstrate that this warm start method significantly improves the success rate and reduces the number of iterations required for the convergence of VQE. The numerical results also indicate that the warm start approach effectively mitigates statistical errors arising from a finite number of measurements, and to a certain extent alleviates the effect of barren plateaus.

quant-ph↗

arXiv2025

Bridging wire and gate cutting with ZX-calculus

Quantum circuit cutting refers to a series of techniques that allow one to partition a quantum computation on a large quantum computer into several quantum computations on smaller devices. This usually comes at the price of a sampling overhead, that is quantified by the $1$-norm of the associated decomposition. The applicability of these techniques relies on the possibility of finding decompositions of the ideal, global unitaries into quantum operations that can be simulated onto each sub-register, which should ideally minimize the $1$-norm. In this work, we show how these decompositions can be obtained diagrammatically using ZX-calculus expanding on the work of Ufrecht et al. [arXiv:2302.00387]. The central idea of our work is that since in ZX-calculus only connectivity matters, it should be possible to cut wires in ZX-diagrams by inserting known decompositions of the identity in standard quantum circuits. We show how, using this basic idea, many of the gate decompositions known in the literature can be re-interpreted as an instance of wire cuts in ZX-diagrams. Furthermore, we obtain improved decompositions for multi-qubit controlled-Z (MCZ) gates with $1$-norm equal to $3$ for any number of qubits and any partition, which we argue to be optimal. Our work gives new ways of thinking about circuit cutting that can be particularly valuable for finding decompositions of large unitary gates. Besides, it sheds light on the question of why exploiting classical communication decreases the 1-norm of a wire cut but does not do so for certain gate decompositions. In particular, using wire cuts with classical communication, we obtain gate decompositions that do not require classical communication.

quant-ph↗

arXiv2025

End-to-End Quantum Algorithm for Topology Optimization in Structural Mechanics

Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we present an end-to-end, fault-tolerant quantum algorithm for topology optimization that operates on the exponential Hilbert space representing the design space. We demonstrate the algorithm on the two-dimensional Messerschmitt-Bölkow-Blohm (MBB) beam problem. By restricting design variables to binary values, we reformulate the compliance minimization task as a combinatorial satisfiability problem solved using Grover's algorithm. Within Grover's oracle, the compliance is computed through the finite-element method (FEM) using established quantum algorithms, including block-encoding of the stiffness matrix, Quantum Singular Value Transformation (QSVT) for matrix inversion, Hadamard test, and Quantum Amplitude Estimation (QAE). The complete algorithm is implemented and validated using classical quantum-circuit simulations. A detailed complexity analysis shows that the method evaluates the compliance of exponentially many structures in quantum superposition in polynomial time. In the global search, our approach maintains Grover's quadratic speedup compared to classical unstructured search. Overall, the proposed quantum workflow demonstrates how quantum algorithms can advance the field of computational science and engineering.

quant-ph↗

arXiv2025

Towards Quantum Algorithms for the Optimization of Spanning Trees: The Power Distribution Grids Use Case

Optimizing the topology of networks is an important challenge across engineering disciplines. In energy systems, network reconfiguration can substantially reduce losses and costs and thus support the energy transition. Unfortunately, many related optimization problems are NP hard, restricting practical applications. In this article, we address the problem of minimizing losses in radial networks, a problem that routinely arises in distribution grid operation. We show that even the computation of approximate solutions is computationally hard and propose quantum optimization as a promising alternative. We derive two quantum algorithmic primitives based on the Quantum Alternating Operator Ansatz (QAOA) that differ in the sampling of network topologies: a tailored sampling of radial topologies and simple sampling with penalty terms to suppress non-radial topologies. We show how to apply these algorithmic primitives to distribution grid reconfiguration and quantify the necessary quantum resources.

eess.SY↗

arXiv2025

Better Embeddings with Coupled Adam

Despite their remarkable capabilities, LLMs learn word representations that exhibit the undesirable yet poorly understood feature of anisotropy. In this paper, we argue that the second moment in Adam is a cause of anisotropic embeddings, and suggest a modified optimizer called Coupled Adam to mitigate the problem. Our experiments demonstrate that Coupled Adam significantly improves the quality of embeddings, while also leading to better upstream and downstream performance on large enough datasets.

cs.CL↗

arXiv2025

Quantum oracles for the finite element method

In order to assess potential advantages of quantum algorithms that require quantum oracles as subroutines, the careful evaluation of the overall complexity of the oracles themselves is crucial. This study examines the quantum routines required for the implementation of oracles used in the block-encoding of the $N \times N$ stiffness and mass matrices, which typically emerge in the finite element analysis of elastic structures. Starting from basic quantum adders, we show how to construct the necessary oracles, which require the calculation of polynomials, square root and the implementation of conditional operations. We propose quantum subroutines based on fixed-point arithmetic that, given an $r$-qubit register, construct the oracle using $\mathcal{O}((K + L + N_{\mathrm{geo}} + N_{\mathrm{D}}) r)$ ancilla qubits and have a $\mathcal{O}((K + L)r^2 + \log_2(N_{\mathrm{geo}} + N_{\mathrm{D}}))$ runtime, with $K$ the order at which we truncate the polynomials, $L$ the number of iterations in the Newton-Raphson subroutine for the square root, while $N_{\mathrm{geo}}$ and $N_{\mathrm{D}}$ are the number of hypercuboids used to approximate the geometry and the boundary, respectively. Since in practice $r$ scales as $r = \mathcal{O}(\log_2 N)$, and assuming that the other parameters are fixed independently of $N$, this shows that the oracles, while still costly in practice, do not endanger potential polynomial or exponential advantages in $N$.

quant-ph↗

arXiv2025

Quantum combinatorial optimization beyond the variational paradigm: simple schedules for hard problems

Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large Hilbert spaces. Hence, finding annealing protocols by variation ultimately appears to be difficult. Similarly, the adiabatic theorem fails on hard problem instances with first-order quantum phase transitions. Here, we show how to use the spin coherent-state path integral to shape the geometry of quantum adiabatic evolution, leading to annealing protocols at polynomial overhead that provide orders-of-magnitude improvements in the probability to measure optimal solutions, relative to linear protocols. These improvements are not obtained on a controllable toy problem but on randomly generated hard instances (Sherrington-Kirkpatrick and Maximum 2-Satisfiability), making them generic and robust. Our method works for large systems and may thus be used to improve the performance of state-of-the-art quantum devices.

quant-ph↗

arXiv2024

Mechanical properties and deformation mechanisms of the C14 Laves and μ-phase in the ternary Ta-Fe(-Al) system

As structural and functional materials, topologically close-packed (TCP) phases of transition metal compounds offer a wide range of attractive properties. Due to their complex crystal structure and the resulting brittleness, the knowledge on their mechanical behaviour is still very limited, especially below the brittle-to-ductile transition temperature. In this study, we systematically analyse the influence of composition and crystal structure on the mechanical properties and deformation mechanisms in the binary Ta-Fe system as well as in the ternary Ta-Fe-Al system as both systems contain a hexagonal C14 Laves and a mu-phase. We use nanoindentation, slip trace analysis and transmission electron microscopy to study the influence of crystal structure, composition and crystal orientation. The composition strongly influences the indentation modulus in the binary Ta-Fe system, showing a decreasing trend with increasing Ta content. The addition of Al, however, does not lead to a significant change of the mechanical properties of the ternary TCP phases. The investigation of the deformation mechanisms revealed that the Laves phase primarily deforms via non-basal slip while the basal plane is the favoured slip plane in the mu-phase. By partly replacing Fe with Al, the plasticity is not affected strongly, but the proportion of non-basal slip slightly increases for both ternary TCP phases compared to the binary ones.

cond-mat.mtrl-sci↗

arXiv2024

Beyond Fundamental Building Blocks: Plasticity in Structurally Complex Crystals

Intermetallics, which encompass a wide range of compounds, often exhibit similar or closely related crystal structures, resulting in various intermetallic systems with structurally derivative phases. This study examines the hypothesis that deformation behavior can be transferred from fundamental building blocks to structurally related phases using the binary samarium-cobalt system. We investigate SmCo$_2$ and SmCo$_5$ as fundamental building blocks and compare them to the structurally related SmCo$_3$ and Sm$_2$Co$_{17}$ phases. Nanoindentation and micropillar compression tests were performed to characterize the primary slip systems, complemented by generalized stacking fault energy calculations via atomic-scale modeling. Our results show that while elastic properties of the structurally complex phases follow a rule of mixtures, their plastic deformation mechanisms are more intricate, influenced by the stacking and bonding nature within the crystal's building blocks. These findings underscore the importance of local bonding environments in predicting the mechanical behavior of structurally related intermetallics, providing crucial insights for the development of high-performance intermetallic materials.

cond-mat.mtrl-sci↗

arXiv2024

Quantum Computing Enhanced Service Ecosystem for Simulation in Manufacturing

Quantum computing (QC) and machine learning (ML), taken individually or combined into quantum-assisted ML (QML), are ascending computing paradigms whose calculations come with huge potential for speedup, increase in precision, and resource reductions. Likely improvements for numerical simulations in engineering imply the possibility of a strong economic impact on the manufacturing industry. In this project report, we propose a framework for a quantum computing-enhanced service ecosystem for simulation in manufacturing, consisting of various layers ranging from hardware to algorithms to service and organizational layers. In addition, we give insight into the current state of the art of applications research based on QC and QML, both from a scientific and an industrial point of view. We further analyse two high-value use cases with the aim of a quantitative evaluation of these new computing paradigms for industrially-relevant settings.

quant-ph↗

arXiv2024

Quantum-Inspired Fluid Simulation of 2D Turbulence with GPU Acceleration

Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which describe a spectrum of fluid phenomena, from the aerodynamics of vehicles to weather patterns. Within this quantum-inspired paradigm, velocity is encoded as matrix product states (MPS), effectively harnessing the analogy between interscale correlations of fluid dynamics and entanglement in quantum many-body physics. This particular tensor structure is also called quantics tensor train (QTT). By utilizing NVIDIA's cuQuantum library to perform parallel tensor computations on GPUs, our adaptation speeds up simulations by up to 12.1 times. This allows us to study the algorithm in terms of its applicability, scalability, and performance. By simulating two qualitatively different but commonly encountered 2D flow problems at high Reynolds numbers up to $1\times10^7$ using a fourth-order time stepping scheme, we find that the algorithm has a potential advantage over direct numerical simulations in the turbulent regime as the requirements for grid resolution increase drastically. In addition, we derive the scaling $χ=\mathcal{O}(\text{poly}(1/ε))$ for the maximum bond dimension $χ$ of MPS representing turbulent flow fields, with an error $ε$, based on the spectral distribution of turbulent kinetic energy. Our findings motivate further exploration of related quantum algorithms and other tensor network methods.

physics.flu-dyn↗

arXiv2024

Measurement-Based Quantum Approximate Optimization

Parameterized quantum circuits are attractive candidates for potential quantum advantage in the near term and beyond. At the same time, as quantum computing hardware not only continues to improve but also begins to incorporate new features such as mid-circuit measurement and adaptive control, opportunities arise for innovative algorithmic paradigms. In this work we focus on measurement-based quantum computing protocols for approximate optimization, in particular related to quantum alternating operator ansätze (QAOA), a popular quantum circuit model approach to combinatorial optimization. For the construction and analysis of our measurement-based protocols we demonstrate that diagrammatic approaches, specifically ZX-calculus and its extensions, are effective for adapting such algorithms to the measurement-based setting. In particular we derive measurement patterns for applying QAOA to the broad and important class of QUBO problems. We further outline how for constrained optimization, hard problem constraints may be directly incorporated into our protocol to guarantee the feasibility of the solution found and avoid the need for dealing with penalties. Finally we discuss the resource requirements and tradeoffs of our approach to that of more traditional quantum circuits.

quant-ph↗

arXiv2023

Diagrammatic Analysis for Parameterized Quantum Circuits

Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis. In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in particular for computing observable expectation values as functions of or for fixed parameters, which are important algorithmic quantities in a variety of applications ranging from combinatorial optimization to quantum chemistry. We provide several new ZX-diagram rewrite rules and generalizations for this setting. In particular, we give formal rules for dealing with linear combinations of ZX-diagrams, where the relative complex-valued scale factors of each diagram must be kept track of, in contrast to most previously studied single-diagram realizations where these coefficients can be effectively ignored. This allows us to directly import a number useful relations from the operator analysis to ZX-calculus setting, including causal cone and quantum gate commutation rules. We demonstrate that the diagrammatic approach offers useful insights into algorithm structure and performance by considering several ansatze from the literature including realizations of hardware-efficient ansatze and QAOA. We find that by employing a diagrammatic representation, calculations across different ansatze can become more intuitive and potentially easier to approach systematically than by alternative means. Finally, we outline how diagrammatic approaches may aid in the design and study of new and more effective quantum circuit ansatze.

quant-ph↗

arXiv2023

Mean-Field Approximate Optimization Algorithm

The Quantum Approximate Optimization Algorithm (QAOA) is suggested as a promising application on early quantum computers. Here, a quantum-inspired classical algorithm, the mean-field Approximate Optimization Algorithm (mean-field AOA), is developed by replacing the quantum evolution of the QAOA with classical spin dynamics through the mean-field approximation. Due to the alternating structure of the QAOA, this classical dynamics can be found exactly for any number of QAOA layers. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick (SK) model and the partition problem, and find that the mean-field AOA outperforms the QAOA in both cases for most instances. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot, i.e. we believe that it will help to identify instances where a true quantum advantage can be expected from the QAOA. To quantify quantum fluctuations around the mean-field trajectories, we solve an effective scattering problem in time, which is characterized by a spectrum of time-dependent Lyapunov exponents. These provide an indicator for the hardness of a given optimization problem relative to the mean-field AOA.

quant-ph↗

arXiv2023

Towards Finding an Optimal Flight Gate Assignment on a Digital Quantum Computer

We investigate the performance of the variational quantum eigensolver (VQE) for the optimal flight gate assignment problem. This problem is a combinatorial optimization problem that aims at finding an optimal assignment of flights to the gates of an airport, in order to minimize the passenger travel time. To study the problem, we adopt a qubit-efficient binary encoding with a cyclic mapping, which is suitable for a digital quantum computer. Using this encoding in conjunction with the Conditional Value at Risk (CVaR) as an aggregation function, we systematically explore the performance of the approach by classically simulating the CVaR-VQE. Our results indicate that the method allows for finding a good solution with high probability, and the method significantly outperforms the naive VQE approach. We examine the role of entanglement for the performance, and find that ansätze with entangling gates allow for better results than pure product states. Studying the problem for various sizes, our numerical data show that the scaling of the number of cost function calls for obtaining a good solution is not exponential for the regimes we investigate in this work.

quant-ph↗

arXiv2022

Withdrawn: A Measurement-based Algorithm for Graph Colouring

In a previous version of this document we misinterpreted the runtime of a part of the described algorithm. Indeed, the runtime is not better than the Grover-Algorithm. We therefor withdraw this work. We present a novel algorithmic approach to find a proper vertex colouring of a graph with $d$ colours, if it exists. We associate a $d$-dimensional quantum system with each vertex and the initial state is a mixture of all possible colourings, from which we obtain a random proper colouring of the graph by measurements. The non-deterministic nature of the quantum measurement is tackled by a reset operation, which can revert the effect of unwanted projections. As in the classical case, we find that the runtime scales exponentially with the number of vertices. However, we provide numerical evidence that the average runtime of the problem-specific part of the algorithm scales polynomially in the number of edges.

quant-ph↗