Quantum scientific computing has emerged as a new paradigm to solve difficult scientific computing problems on quantum computers. One of them is topology optimization, which is computationally expensive because the combinatorial optimization problem and partial differential equations need to be solved simultaneously. In this paper, we propose a novel variational quantum algorithm for topology optimization through quantum entanglement. Two quantum registers are used to encode the optimal configurations and the solutions to physical constraints, respectively. The tasks of finding the optimal material configuration and solving the physical constraints are performed simultaneously in a single loop. A constraint encoding scheme is also proposed to incorporate volume and topology constraints in optimization. The gate complexity of the proposed quantum algorithm is analyzed. The theoretical lower bound of the success probability is obtained. The algorithm is demonstrated with compliance minimization problems including truss structures and Messerschmitt-Bölkow-Blohm beams.
Quantum scientific computing has emerged as a new paradigm to solve difficult scientific computing problems on quantum computers. One of them is topology optimization, which is computationally expensive because the combinatorial optimization problem and partial differential equations need to be solved simultaneously. In this paper, we propose a novel variational quantum algorithm for topology optimization through quantum entanglement. Two quantum registers are used to encode the optimal configurations and the solutions to physical constraints, respectively. The tasks of finding the optimal material configuration and solving the physical constraints are performed simultaneously in a single loop. A constraint encoding scheme is also proposed to incorporate volume and topology constraints in optimization. The gate complexity of the proposed quantum algorithm is analyzed. The theoretical lower bound of the success probability is obtained. The algorithm is demonstrated with compliance minimization problems including truss structures and Messerschmitt-Bölkow-Blohm beams.
Abstract One of the challenging scientific computing problems is topology optimization (TO), where the two tasks of searching through the combinatorially complex configurations and solving the constraints of partial differential equations need to be done simultaneously. In this paper, a novel variational quantum algorithm for constrained TO is proposed, which allows for the single-loop parallel search for the optimal configuration that also satisfies the physical constraints. The optimal configurations and the solutions to physical constraints are encoded with two separate quantum registers. A constraint encoding scheme is also proposed to incorporate volume and connectivity constraints in optimization. The gate complexity of the proposed quantum algorithm is analyzed. The algorithm is demonstrated with compliance minimization problems including truss structures and Messerschmitt–Bölkow–Blohm beams.
Product development processes frequently use numerical simulations and mathematical programming techniques. Structural optimization, especially topology optimization, is one of the most promising techniques for generating insightful design choices. Topology optimization for discrete structures, such as truss structures, can be formulated as a combinatorial optimization problem, where the combination of the existence or absence of the material is optimized. In this study, we examine the usage of quantum computers as a potential solution to discrete topology optimization problems. The proposed method consists of two variational quantum algorithms (VQAs); the first solves the state equilibrium equation for all possible structures, and the second amplifies the probability of the optimal structure in quantum superposition. Several experiments, including a real device experiment, show that the proposed method successfully obtained the optimal structure. These findings suggest that quantum computers could be a potential tool for solving topology optimization problems.
Quantum computing has become a pivotal innovation in computational science, offering novel avenues for tackling the increasingly complex and high-dimensional optimization challenges inherent in engineering design. This paradigm shift is particularly pertinent in the domain of structural optimization, where the intricate interplay of design variables and constraints necessitates advanced computational strategies. In this vein, the gate-based variational quantum algorithm utilizes quantum superposition and entanglement to improve search efficiency in large solution spaces. This paper delves into the gate-based variational quantum algorithm for the discrete variable truss structure size optimization problem. By reformulating this optimization challenge into a quadratic, unconstrained binary optimization framework, we bridge the gap between the discrete nature of engineering optimization tasks and the quantum computational paradigm. A detailed algorithm is outlined, encompassing the translation of the truss optimization problem into the quantum problem, the initialization and iterative evolution of a quantum circuit tailored to this problem, and the integration of classical optimization techniques for parameter tuning. The proposed approach demonstrates the feasibility and potential of quantum computing to transform engineering design and optimization, with numerical experiments validating the effectiveness of the method and paving the way for future explorations in quantum-assisted engineering optimizations.
This paper introduces a novel geometric topology optimization algorithm leveraging quantum computing to address complex optimization problems. Traditional optimization methods rely on manual constraint design, limiting flexibility and computational efficiency. We propose a quantum-enhanced approach that dynamically adjusts geometric constraints and utilizes quantum entanglement to explore the intricate structure of geometric topologies. This algorithm demonstrates significant improvements in optimization speed and solution quality compared to classical methods for a range of geometric constraint problems. The core mechanism involves utilizing quantum entanglement to represent and manipulate the underlying topology, enabling efficient exploration of the solution space. This research presents a fundamentally new approach to geometric optimization, potentially revolutionizing the field through enhanced computational power and algorithmic efficiency.
This paper introduces a novel framework for topology structure optimization based on quantum entanglement. Traditional optimization methods often struggle with complex physical systems due to the limitations of predefined parameters. Quantum entanglement offers a unique mechanism to simulate physical phenomena, enabling automated adjustments to topology and, consequently, optimized results. We propose a new algorithm leveraging entangled states to guide the search for optimal physical configurations, demonstrating its potential for surpassing conventional approaches. The core mechanism utilizes entanglement to dynamically explore the solution space, leading to a more robust and efficient optimization process. We provide a detailed explanation of the algorithm's steps, including the entanglement initialization and the iterative adjustment process. This research explores the practical implications of this approach, showcasing its ability to generate novel and potentially advantageous physical configurations.
Abstract 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 an exponentially large Hilbert space representing the design space. We demonstrate the algorithm on the two-dimensional Messerschmitt-Bölkow-Blohm 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 using established quantum algorithms, including block-encoding of the stiffness matrix, quantum singular value transformation for matrix inversion, Hadamard test, and quantum amplitude estimation. 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.