Optimization

Ferdi Güler, Batuhan Selamoglu

Purpose: The development of engineering decision support systems requires effective optimization techniques to deal with complex optimization problems such as energy management, logistics optimization, and resource management. The most popular classical optimization techniques, such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), are often less effective in terms of optimization performance and are often likely to suffer from slow optimization speed and premature convergence to local optima when dealing with highdimensional optimization search space. The quantum-inspired optimization (QIO) techniques are an emerging class of optimization techniques that attempt to mimic some principles of quantum computing on classical computers to overcome the limitations of classical optimization techniques. The purpose of this research is to develop a quantum-inspired optimization framework to overcome the limitations of classical optimization techniques in engineering decision support systems. Method: The proposed optimization framework incorporates a probabilistic amplitude representation of solutions, rotation-based evolutionary optimization, and simulated annealing acceptance criteria. The optimization framework was tested on two optimization scenarios: a highdimensional optimization problem inspired by a Rastrigin-like function representing energy management optimization and a multi-objective optimization problem inspired by logistics optimization with the goal of minimizing transportation costs and time. The optimization performance and effectiveness of the proposed optimization framework were compared with classical optimization techniques such as GA and PSO. Findings: The proposed optimization framework outperforms traditional methods such as GA and PSO in terms of speed and quality of results. In the high-dimensional problem, the proposed framework achieved an optimal value of 38.96, which is better compared to the results of PSO, which achieved 69.42, and GA, which achieved 137.22. In the multi-objective problem, the proposed framework achieved Pareto results, which show better performance and effectiveness compared to the traditional methods. Conclusion: The optimization results indicate that the quantum-inspired optimization framework is an effective optimization tool that can be used to overcome the limitations of classical optimization techniques in engineering decision support systems. The proposed optimization framework provides a link between classical optimization techniques and emerging quantum optimization techniques while being able to run on classical computers.

O. Costa de Beauregard

Jatin Arora, Mingkuan Xu, Sam Westrick +4 more

Recent advances in quantum architectures and computing have motivated the development of new optimizing compilers for quantum programs or circuits. Even though steady progress has been made, existing quantum optimization techniques remain asymptotically and practically inefficient and are unable to offer guarantees on the quality of the optimization. Because many global quantum circuit optimization problems belong to the complexity class QMA (the quantum analog of NP), it is not clear whether quality and efficiency guarantees can both be achieved. In this paper, we present optimization techniques for quantum programs that can offer both efficiency and quality guarantees. Rather than requiring global optimality, our approach relies on a form of local optimality that requires each and every segment of the circuit to be optimal. We show that the local optimality notion can be attained by a cut-and-meld circuit optimization algorithm. The idea behind the algorithm is to cut a circuit into subcircuits, optimize each subcircuit independently by using a specified "oracle" optimizer, and meld the subcircuits by optimizing across the cuts lazily as needed. We specify the algorithm and prove that it ensures local optimality. To prove efficiency, we show that, under some assumptions, the main optimization phase of the algorithm requires a linear number of calls to the oracle optimizer. We implement and evaluate the local-optimality approach to circuit optimization and compare with the state-of-the-art optimizers. The empirical results show that our cut-and-meld algorithm can outperform existing optimizers significantly, by more than an order of magnitude on average, while also slightly improving optimization quality. These results show that local optimality can be a relatively strong optimization criterion and can be attained efficiently.

Siyi Wang, Anupam Chattopadhyay

Jatin Arora, Mingkuan Xu, Sam Westrick +4 more

Recent advances in quantum architectures and computing have motivated the development of new optimizing compilers for quantum programs or circuits. Even though steady progress has been made, existing quantum optimization techniques remain asymptotically and practically inefficient. Because many global quantum circuit optimization problems belong to the complexity class QMA (the quantum analog of NP) [51], it is not clear whether efficiency guarantees can be achieved. In this paper, we present an algorithm that achieves efficiency by aiming at a form of local optimality rather than global optimality. Our local-optimization algorithm cuts a circuit into subcircuits, optimizes each subcircuit with the specified oracle optimizer, and melds the subcircuits by optimizing across the cuts lazily as needed. To prove efficiency, we show that, under some assumptions, the main optimization phase of the algorithm requires a linear number of calls to the oracle optimizer. Our empirical results show that our local-optimization algorithm can outperform existing optimizers significantly, by more than an order of magnitude on average. Perhaps surprisingly, the algorithm achieves these improvements without noticeable degradation in optimization quality. These results show that local optimization can be effective for optimizing quantum circuits.