Convergence of the quantum dynamics framework for optimization algorithm

Sergio Boixo, Gerardo Ortíz, Rolando D. Somma

Jincheng Zhang

This paper explores the potential of Dynamic Quantum Feedback Loops (DQFLs) to enhance the convergence of algorithmic processes. Classical algorithms frequently encounter difficulties in achieving optimal performance, necessitating innovative approaches. We propose a novel system where the algorithm's own parameters are dynamically adjusted based on performance feedback, fostering an iterative refinement process. This investigation focuses on the design and implementation of a DQFL framework, examining its impact on algorithm convergence speed and stability through theoretical analysis and simulation. The core principle is to leverage quantum-inspired feedback to guide the algorithm towards a more stable and efficient state.

Ansh Bansal

Limeng Luo, Peng Wang, Minghui Zhao

With the emergence of various optimization algorithms, studying the specific dynamic evolution process of algorithms is of significant importance for proposing new algorithms and optimizing classical ones. The Quantum Dynamics Framework(QDF) Optimization Algorithm is derived from the Taylor expansion of the Schrödinger equation, providing a rigorous mathematical and physical foundation. Its iterative behavior can reflect the generality of evolution in most optimization algorithms. However, the iteration process of QDF on the multi-modal Rastrigin function faces challenges in convergence, necessitating meticulous evaluation and research of test functions. Therefore, this paper constructs an adjustable, scalable, and diverse Rastrigin-like Test Benchmark (RTB) collection, extending, shifting, and rotating the Rastrigin function in multi-modal scenarios. By viewing the algorithm's iteration process from the perspective of quantum dynamics as the evolution of sampling particles over time, and utilizing RTB to delve into the dynamical behavior of QDF algorithm, this research approach effectively supports the observation and improvement of algorithmic iteration processes, providing fundamental guidance for algorithmic optimization decisions.

Haijiang Kou, Yaowen Zhang, Heow Pueh Lee

Bruno O. Fernandez, Rodrigo Bloot, Marcelo Albano Moret

Binary optimization problems are emerging as potential candidates for useful applications of quantum computing. Among quantum algorithms, the quantum approximate optimization algorithm (QAOA) is currently considered the most promising method to obtain a quantum advantage for such problems. The QAOA method uses a classical counterpart to perform optimization in a hybrid approach. In this paper, we show that the recently introduced method called quantum circuit evolutionary (QCE) also has potential for applications in binary optimization problems. This methodology is classical optimizer-free, but, for some scenarios, may have convergence stagnation as a consequence of smooth circuit modifications at each generation. To avoid this drawback and accelerate the convergence capabilities of QCE, we introduce a framework using an adaptive cost function (ACF), which varies dynamically with the circuit evolution. This procedure accelerates the convergence of the method. Applying this new approach to instances of the set partitioning problem, we show that QCE-ACF achieves convergence performance identical to QAOA but with a shorter execution time. Finally, experiments in the presence of induced noise show that this framework is quite suitable for the noisy intermediate-scale quantum era.