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Topology Optimization powered by Quantum for smarter, faster engineering simulations

Updated: Mar 14, 2023

Topology optimization is a powerful computational method used to determine the optimal shape of a structure to achieve specific performance goals. It involves generating, evaluating, and iterating multiple designs to optimize for objectives and constraints. It can minimize material usage, reduce weight, or increase strength. This technique has proven extremely useful across various industries, including aerospace, automotive, architecture, and Design manufacturing.

It can help design lightweight yet vital aircraft components in aerospace. As a result, fuel efficiency can be increased by minimizing the material and mass used in aircraft structures leading to significant cost savings. Similarly, in the automotive industry, topology optimization reduces the weight of chassis, suspension systems, and other components without compromising structural strength and integrity. Optimizing for high stiffness to weight is ideal for better vehicle performance and handling.

Topology optimization in construction engineering can optimize the shape of buildings for various factors such as wind load, solar gain, and structural stability. This approach can result in more efficient use of building materials and reduced construction costs.

Currently, topology optimization on CAE software uses classical gradient-based or non-gradient-based techniques or algorithms. However, both classical Gradient Topology Optimization and Non-Gradient Topology Optimization methods have limitations. These include high computation power and slow convergence to optimal solutions, particularly for large-scale complex simulations with multiple variables.

Figure: Challenges with classical GTO and NGTO

Leveraging the power of Quantum Computing for Topology Optimization

Complex engineering requires fast, efficient full-scale optimization within a more extensive search space. One major bottleneck is the computational time to perform many design iterations to identify the optimal solution. Furthermore, numerous constraints and variables must be considered as the complexity of engineering increases, and some of these boundary conditions need to be revised to model with traditional computing. Therefore, the accuracy of the results is highly dependent on the time required to evaluate the performance of numerous design iterations with the current limitations of computational resources.

Quantum computing has the potential to overcome these limitations by leveraging the parallel processing power of Quantum bits or qubits. In addition, because qubits can exist in multiple states simultaneously, Quantum computers can evaluate numerous design options simultaneously, reducing the time required for optimization.

Several research initiatives already aim to use Quantum computing to improve topology optimization, including collaborations between academic institutions and industry leaders such as Airbus and BMW. These efforts focus on developing quantum algorithms and optimization strategies to handle large-scale problems while efficiently providing accurate and reliable results.

Upping the ante: BQP's disruptive approach

BosonQ Psi's disruptive simulation suite BQPhy® has implemented an innovative approach based on modified Quantum-inspired evolutionary algorithms (non-gradient optimization). The goals are to meet industries' current and future CAE simulation needs, such as reducing product recall and reducing manufacturing costs and time-to-market. For example, in applications like automotive and aerospace, topology optimization needs to be quick, precise, and satisfy multiple boundary conditions.

Quantum Inspired Optimization emulates Quantum effects and leads to new Quantum-based solutions for optimization problems. Quantum Inspired Evolutionary algorithms (QIEA) solve these optimization problems (Quantum Inspired Evolutionary Optimization - (QIEO). In addition, QIEO provides robustness in finding solutions in certain use cases specific to industrial applications.

Applicability of BQP's Quantum Inspired Evolutionary Optimization (QIEO)

Quantum-inspired optimization methods are heuristic. As a result, they find the best solution and consistently outperform conventional optimization approaches when Optimization landscapes are complex but structured and organized. Such landscapes are typical in the real world. Simplistic algorithms are adequate if the number of variables is limited (for example, fewer than one hundred). However, Quantum-inspired optimization has significantly outperformed the classical approach for problems with hundreds of variables.

How it works

BosonQ Psi's (BQP) quantum-powered simulation software suite BQPhy® uses the Quantum-inspired approach to create multiple candidates, like traditional evolutionary methods. First, these candidates are encoded into a Quantum register and converted into binary data to expand the candidate pool. Then, the Quantum parameters are manipulated to generate additional candidates until the optimized criteria are satisfied.

Benchmarking of QIEO with Rosenbrock function & Holder Table Function:

Rosenbrock function -

The Rosenbrock function is a mathematical function frequently used to test the performance of optimization algorithms. It is non-convex, which means it has a complex shape with multiple peaks and valleys. The plot shows a contour space map for the Rosenbrock Function; it shows the darker region has a lower value of f(x, y), which we are trying to find.

Holder Table Function

The Holder Table function is a prevalent optimization problem that contains numerous local minima. Despite this, it has four global minima, the lowest function values across the entire domain.

The global minimum is inside a long, narrow, parabolic-shaped, flat valley. To find the valley is trivial. To converge to the global minimum, however, is difficult. The figure below shows a minimization problem that minimizes the value of f(x, y) for finding global minima.


The figure shows a red cross in the center, indicating the local minima found using classical algorithms. A blue cross is encircled at each of the four corners, representing the global minima. BQPhy®-QIEO algorithm was able to identify four global minima efficiently.

This algorithm can explore a more extensive search space, increasing the exploration rate and allowing for more rigorous constraint evaluations, enabling efficient simulation.

An analogy to describe this difference is like exploring a forest with a headlamp, representing the classical approach focused only in one direction. However, BQPhy®-QIEO can be equated to night vision that offers a broader view. As a result, it enables a more comprehensive exploration of the area and identifies more solutions.

Performance comparisons

The result shows that BQPhy®’s QIEO converged with fewer solutions generated (<50 iterations) and converged faster than gradient-based and simulated annealing approaches. Furthermore, it indicates that BQP’s QIEO requires less computational resources to generate optimal solutions more quickly than traditional approaches, which has higher significance on the industrial application like applications in Topology Optimization & Design Optimization in the automotive industry, aerospace industry, and others.

Use cases of BQPhy®-QIEO:

Topology Optimization:

Reduction of weight from the control arm BQPhy®’s QIEO, the QIEO approach reduced the weight by 3.2 times more than traditional approaches with 8x less computational resources.

Figure: Mass Optimization of Control arm

Figure: Shape optimization of an airfoil of a racecar using BQP-QIEO (Redline)

BQPhy®'s QIEO approach explores a more extensive search space for optimal solutions, making it efficient for optimizing multivariable problems. In addition, this approach allows for the simultaneous exploration of designs, leading to efficient optimization using the same or fewer computational resources. This approach resulted in 18% better optimization than traditional methods, leading to 40% cost savings.

Applying this approach can result in lighter and stronger components for various use cases, making it beneficial in complex and competitive Airline & Aerospace, heavy engineering, and automotive industries.

The potential of Quantum for complex simulations

By leveraging the unique properties of quantum mechanics, Quantum computing has the potential to speed up complex simulations and overcome the computational bottleneck exponentially.

BQP proprietary algorithms and software tools enable the integration of Quantum computing with existing classical computing infrastructure, such as cloud platforms, high-performance computing clusters, and data analytics frameworks.

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